Information Technologies in Biomedicine: Volume 2 (Advances in Intelligent and Soft Computing, 69)

Advances in Intelligent and Soft Computing Editor-in-Chief: J. Kacprzyk

69

Advances in Intelligent and Soft Computing Editor-in-Chief Prof. Janusz Kacprzyk Systems Research Institute Polish Academy of Sciences ul. Newelska 6 01-447 Warsaw Poland E-mail: [email protected] Further volumes of this series can be found on our homepage: springer.com Vol. 54. B.-y. Cao, C.-y. Zhang, T.-f. Li (Eds.) Fuzzy Information and Engineering, 2009 ISBN 978-3-540-88913-7 Vol. 55. Y. Demazeau, J. Pavón, J.M. Corchado, J. Bajo (Eds.) 7th International Conference on Practical Applications of Agents and Multi-Agent Systems (PAAMS 2009), 2009 ISBN 978-3-642-00486-5 Vol. 56. H. Wang, Y. Shen, T. Huang, Z. Zeng (Eds.) The Sixth International Symposium on Neural Networks (ISNN 2009), 2009 ISBN 978-3-642-01215-0 Vol. 57. M. Kurzynski, M. Wozniak (Eds.) Computer Recognition Systems 3, 2009 ISBN 978-3-540-93904-7 Vol. 58. J. Mehnen, A. Tiwari, M. Köppen, A. Saad (Eds.) Applications of Soft Computing, 2009 ISBN 978-3-540-89618-0 Vol. 59. K.A. Cyran, S. Kozielski, J.F. Peters, U. Sta´nczyk, A. Wakulicz-Deja (Eds.) Man-Machine Interactions, 2009 ISBN 978-3-642-00562-6 Vol. 60. Z.S. Hippe, J.L. Kulikowski (Eds.) Human-Computer Systems Interaction, 2009 ISBN 978-3-642-03201-1 Vol. 61. W. Yu, E.N. Sanchez (Eds.) Advances in Computational Intelligence, 2009 ISBN 978-3-642-03155-7

Vol. 62. B. Cao, T.-F. Li, C.-Y. Zhang (Eds.) Fuzzy Information and Engineering Volume 2, 2009 ISBN 978-3-642-03663-7 Vol. 63. Á. Herrero, P. Gastaldo, R. Zunino, E. Corchado (Eds.) Computational Intelligence in Security for Information Systems, 2009 ISBN 978-3-642-04090-0 Vol. 64. E. Tkacz, A. Kapczynski (Eds.) Internet – Technical Development and Applications, 2009 ISBN 978-3-642-05018-3 Vol. 65. E. Kacki, ˛ M. Rudnicki, J. Stempczy´nska (Eds.) Computers in Medical Activity, 2009 ISBN 978-3-642-04461-8 Vol. 66. G.Q. Huang, K.L. Mak, P.G. Maropoulos (Eds.) Proceedings of the 6th CIRP-Sponsored International Conference on Digital Enterprise Technology, 2009 ISBN 978-3-642-10429-9 Vol. 67. V. Snášel, P.S. Szczepaniak, A. Abraham, J. Kacprzyk (Eds.) Advances in Intelligent Web Mastering - 2, 2010 ISBN 978-3-642-10686-6 Vol. 68. V.-N. Huynh, Y. Nakamori, J. Lawry, M. Inuiguchi (Eds.) Integrated Uncertainty Management and Applications, 2010 ISBN 978-3-642-11959-0 Vol. 69. E. Pi˛etka and J. Kawa (Eds.) Information Technologies in Biomedicine, 2010 ISBN 978-3-642-13104-2

Ewa Pi˛etka and Jacek Kawa (Eds.)

Information Technologies in Biomedicine Volume 2

ABC

Editors Prof. Ewa Pi˛etka Silesian University of Technology Faculty of Automatic Control Electronics and Computer Science ul. Akademicka 16 44-100 Gliwice Poland E-mail: [email protected] Prof. Jacek Kawa Silesian University of Technology Faculty of Automatic Control Electronics and Computer Science ul. Akademicka 16 44-100 Gliwice Poland E-mail: [email protected]

ISBN 978-3-642-13104-2

e-ISBN 978-3-642-13105-9

DOI 10.1007/978-3-642-13105-9 Advances in Intelligent and Soft Computing

ISSN 1867-5662

Library of Congress Control Number: Applied for c 

2010 Springer-Verlag Berlin Heidelberg

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typeset & Cover Design: Scientific Publishing Services Pvt. Ltd., Chennai, India. Printed on acid-free paper 543210 springer.com

Foreword

Significant development in medical diagnosis and therapy, observed in recent years, is undoubtedly connected with the development of computer systems of information processing on the basis of the improvement of technology and construction of electronic devices, application of theory and appropriate algorithms as well as development of tools used in the software development process. Possible benefits obtained in all branches of medicine are unquestionable. The progress of civilization results in an increase of the disease rate in muscoskeletal and cardiovascular systems, tumours being predominant in medical statistics. Furthermore, factors concerning aging of population, traffic accidents, sports activity, in particular extreme sports, demand modern medical techniques and technologies. The solution of complex problems concerning diagnostics and medical therapy is possible thanks to the development of interdisciplinary cooperation of experts from diverse branches of medical and engineering fields. The engineering knowledge defined as biomedical engineering is covering biosystems, biomaterials, biomechanics and rehabilitation engineering, biomedical imaging as well as computer and telemedicine systems, neural networks and medical physics. The development of biomedical engineering undoubtedly reflects the present state of the art and knowledge of biological reality. Mainly, it depends on the application of new cognitive and diagnostic methods that use the latest achievements from the field of natural sciences and technology. Issues concerning biomedical engineering are actively developed in many scientific and clinical centres all over the world, which is manifested by a stream of reports, publications and papers. Thus, their periodic analysis and synthesis is required. In consequence, comprehensive studies enriching the present state of the art are published. The studies will be useful in the

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Foreword

arrangement of knowledge and its application, in the production of medical devices and the elaboration of innovative diagnostic and therapeutic procedures in clinical practice. The papers presented in this book are pursuing the above denoted aims. Gliwice, June 2010

Jan Marciniak

Preface

Information Technology in Biomedicine is an interdisciplinary research area, that bridges the gap between methodological achievements in engineering and clinical requirements in medical diagnosis and therapy. It is an emerging field focusing on collaboration between physicians, scientists, and technicians in order to define and meet patients needs. Many of these areas are recognized as research and development frontiers in employing new technology in clinical environment. These include image-guided diagnosis and treatment, biotechnology, biomaterials, biometrics, telemedicine and home care. New approaches to information technologies increase the efficiency of medical diagnostic and treatment and permit more information to be extracted from the acquired data. In this book, members of the academic society of technical and medical background present their research results and clinical implementation in order to satisfy the functional requirements of authorized physicians for the benefit of the patients. An extended area is covered by the articles. It includes biomedical signals, medical image processing, computer-aided diagnosis and surgery, biometrics, healthcare and telemedicine, biomechanics, biomaterials, bioinformatics. Section on bronchoscopy presents the basis as well as new research studies performed in this field. Papers present various theoretical approaches and new methodologies based on fuzzy sets, mathematical statistics, mathematical morphology, fractals, wavelets, syntactic methods, artificial neural networks, graphs and many others. We would like to express our gratitude to all paper reviewers as well as the authors who have contributed their original research papers. Gliwice, June 2010

Ewa Pietka  Jacek Kawa

Contents

Part I: Image Processing and CAD On a Hybrid Fuzzy Clustering Method . . . . . . . . . . . . . . . . . . . . . . Tomasz Przybyla, Janusz Je˙zewski, Dawid Roj 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Generalized Cost Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Weighted Myriad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Weighted Meridian . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Generalized Cost Function . . . . . . . . . . . . . . . . . . . . . 3 Hybrid Clustering Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Data Clustering with the Hybrid Clustering Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Numerical Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Complete Gradient Clustering Algorithm for Features Analysis of X-Ray Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Malgorzata Charytanowicz, Jerzy Niewczas, Piotr Kulczycki, ˙ Piotr A. Kowalski, Szymon L  ukasik, Slawomir Zak 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Complete Gradient Clustering Algorithm (CGCA) . . . . . . . . 2.1 Kernel Density Estimation . . . . . . . . . . . . . . . . . . . . . 2.2 Procedures of the CGCA . . . . . . . . . . . . . . . . . . . . . . 3 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 3 4 4 6 8 10 11 12 13 14 15

15 16 16 18 19 20 23 24

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Dynamics of the Clusterization Process in an Adaptative Method of Image Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Aleksander Lam˙za, Zygmunt Wr´ obel 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Definitions and Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Segmentation Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Generating the Initial Set of Clusters . . . . . . . . . . . . 3.2 Merging the Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Adaptation of the Threshold Variance . . . . . . . . . . . 3.4 Dynamics of the Merging Process . . . . . . . . . . . . . . . 4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Application of Adaptive Weighed Averaging to Digital Filtering of 2D Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Alina Momot 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Weighted Averaging Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 EBWA Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Adaptive Linear Spatial Filtering . . . . . . . . . . . . . . . 3 Numerical Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Experiments with Salt-and-Pepper Noise . . . . . . . . . 3.2 Experiments with Gaussian Noise . . . . . . . . . . . . . . . 4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Photodynamic Image e-Atlas in Diagnostic and Treatment Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ewa Pietka, Aleksander Sieron, Dominik Spinczyk, Przemyslaw Szabelak, Sebastian Kwiatek, Jakub Murawski 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Acquisition Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Image Archive and Presentation Module . . . . . . . . . . . . . . . . 4 Computer Aided Diagnosis and Therapy . . . . . . . . . . . . . . . . 5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Multiseries MR Data in Brain Tumours Segmentation . . . . . . . Jacek Kawa, Pawel Szwarc, Barbara Bobek-Billewicz, Ewa Pietka  1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Brain Tumours . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Nature of MR Imaging Data . . . . . . . . . . . . . . . . . . . 1.3 Brain Tumour Segmentation Approaches . . . . . . . . . 2 Segmentation Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25 25 26 26 27 27 28 30 32 32 33 33 35 35 36 37 37 40 44 44 45

45 46 46 49 51 52 52 53 53 54 54 55 55

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2.1

Segmentation of Contrast Enhanced T1W Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Perfusion Maps Analysis . . . . . . . . . . . . . . . . . . . . . . . 3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Symmetry Plane of the Brain on Perfusion MR Images . . . . . . Rafal Henryk Kartaszy´ nski, Pawel Mikolajczak 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Data Preprocessing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Finding Characteristic Points . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Perpendicular Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Results and Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A Two-Step Method for Detection of Architectural Distortions in Mammograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Magdalena Jasionowska, Artur Przelaskowski, Aleksandra Rutczynska, Anna Wroblewska 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Architectural Distortion . . . . . . . . . . . . . . . . . . . . . . . 2 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 ArDist Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 GF Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 DD Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Results of ArDist Method . . . . . . . . . . . . . . . . . . . . . . 4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . An Instrument for Monitoring Inflow and Washout of an Optical Contrast Agent into the Brain . . . . . . . . . . . . . . . . . . . . . . . ˙ lek, Piotr Sawosz, Daniel Milej, Michal Kacprzak, Norbert Zo Roman Maniewski, Adam Liebert 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Discussion and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4D Segmentation of Ewing’s Sarcoma in MR Images . . . . . . . . . Joanna Czajkowska, Pawel Badura, Ewa Pietka 1 Ewing’s Sarcoma Segmentation Problem . . . . . . . . . . . . . . . . 2 ROI Detection, Fuzzy C-Means Clustering . . . . . . . . . . . . . . .

56 57 59 63 63 65 65 66 67 68 69 70 72 72 73

73 74 74 76 77 79 82 83 84 85

85 86 88 88 89 91 91 93

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3 Gaussian Mixture Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 4 Fuzzy Connectedness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 5 Transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 Segmentation of Stained Lymphoma Tissue Section Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Urszula Neuman, Anna Korzynska, Carlos Lopez, Marylene Lejeune 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Algorithm Description . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Algorithm Implementation . . . . . . . . . . . . . . . . . . . . . 3.3 Evaluation of the Proposed Method . . . . . . . . . . . . 3.4 Sample and Image Acquisition . . . . . . . . . . . . . . . . . . 4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Anterior and Posterior Cruciate Ligament – Extraction and 3D Visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Piotr Zarychta, Anna Zarychta-Bargiela 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Location of the Cruciate Ligament Structure on the T1W MR Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Extraction of the Cruciate Ligament Structure from the T1W MR Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Numerical Results and Conclusion . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Computerized Evaluation of Abnormal Hand Bone Patterns in Skeletal Dysplasias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Arkadiusz Gertych, Morgan Clond, Ralph Lachman, David Rimoin 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

101 101 103 104 105 107 107 108 109 109 110 111 115 115 117 118 120 122 123 124 124 125 127 128 131

Contents

Method of Brain Structure Extraction for CT-Based Stroke Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Aleksandra Rutczy´ nska, Artur Przelaskowski, Magdalena Jasionowska, Grzegorz Ostrek 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Stochastic Image Modeling . . . . . . . . . . . . . . . . . . . . . 3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Combined DICOM and HL7 Viewer in Support of a Bridge from Content-Based Image Retrieval to Computer-Aided Diagnosis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Petra Welter, Fatih Topal, Sebastian Jansen, Thomas M. Deserno, J¨ org Riesmeier, Christoph Grouls, Rolf W. G¨ unther 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 CBIR-Based CADx Scheme . . . . . . . . . . . . . . . . . . . . 2.2 DICOM SR Encoded CBIR Results . . . . . . . . . . . . . 2.3 Query of HL7 Diagnostic Findings . . . . . . . . . . . . . . 2.4 Mapping of DICOM and HL7 Identifiers . . . . . . . . . 2.5 Analysis of Data Capture Process . . . . . . . . . . . . . . . 3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 System Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Implementation of IRMACON Viewer . . . . . . . . . . . 3.3 Layout of IRMACON Viewer . . . . . . . . . . . . . . . . . . . 4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3D Diagnostic System for Anatomical Structures Detection Based on a Parameterized Method of Body Surface Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wojciech Glinkowski, Jakub Michonski, Robert Sitnik, Marcin Witkowski 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Telescreening Diagnostic System . . . . . . . . . . . . . . . . . . . . . . . 2.1 Measurement System . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Database . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Calculation and Diagnosis Support . . . . . . . . . . . . . . 3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

XIII

133

133 135 136 139 141 143

145

145 147 147 147 147 148 148 149 149 150 150 151 151

153

154 155 156 158 160 162 162

XIV

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Reconstruction of the Pelvic Region Based on the Statistical Shape Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pawel Skadlubowicz, Zdzislaw Krol, Zygmunt Wrobel, Fritz Hefti, Andreas Krieg 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Conclusions and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Automatic Measuring of the Iridocorneal Angle in the Optical Coherence Tomographic Image of the Anterior Segment of the Eye . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Robert Koprowski, Zygmunt Wrobel, Anna Nowinska, Edward Wylegala 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Image Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Existing Methods of the Iridocorneal Angle Analysis . . . . . . 4 Results Obtained by Existing Algorithms . . . . . . . . . . . . . . . . 5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Parametric Curves in Liver Deformation for Laparoscopic Purposes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Monika Bugdol, Jan Juszczyk 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Data Collecting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Deformation Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Future Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fractal Analysis of Dental Radiographic Images in the Irregular Regions of Interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Edward Oczeretko, Marta Borowska, Izabela Szarmach, Agnieszka Kitlas, Janusz Szarmach, Andrzej Radwa´ nski 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Practical Assessment of Fractal Dimension . . . . . . . . . . . . . . 2.1 Rectangular Prism Surface Area Method — “Skyscraper Method” . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Triangular Prism Surface Area Method . . . . . . . . . . 2.3 Intensity Difference Scaling Method . . . . . . . . . . . . . 3 Irregular Regions of Interest . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Experiments – Intensity Difference Scaling Method . . . . . . . 4.1 Magnetic Resonance Image . . . . . . . . . . . . . . . . . . . . . 4.2 Pantomogram (Panoramic Radiograph) . . . . . . . . . .

165

165 166 169 172 172

175

175 177 178 178 182 182 183 183 184 185 188 189 189 191

191 193 193 194 194 195 196 196 196

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4.3 Dental Radiovisiographic Image . . . . . . . . . . . . . . . . . 197 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 Part II: Computer Aided Surgery Computer-Assisted Navigation in Brain Tumor Surgery . . . . . Zbigniew Kotwica, Agnieszka Saracen 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Clinical Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Procedures Performed . . . . . . . . . . . . . . . . . . . . . . . . . 3 Discussion and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Computer Aided Alternative Methods of Dental Implants Placement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ˙ Jaroslaw Zmudzki 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

203 204 205 205 209 209 211 211 212 214 215 216

Part III: Biometrics An Idea of Human Voice Reaction Measurement System under the Aspect of Behavioral Biometric . . . . . . . . . . . . . . . . . . . Andrzej W. Mitas, Marcin D. Bugdol 1 Behavioral Biometric – Introduction . . . . . . . . . . . . . . . . . . . . 2 Structure of the Measurement System . . . . . . . . . . . . . . . . . . . 2.1 Hardware and Software . . . . . . . . . . . . . . . . . . . . . . . . 3 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Biomedically Aided Car Driver Safety System . . . . . . . . . . . . . . . Andrzej W. Mitas, Artur Rygula 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Standardization of Driver’s Road Behaviours . . . . . . . . . . . . 3 The Analysis of Driver’s Behaviours . . . . . . . . . . . . . . . . . . . . 4 Biocybernetics System of Driving Behaviours Analysis . . . 4.1 Psycho-physiological State Determination . . . . . . . . 4.2 Proposition of Measurement System . . . . . . . . . . . . . 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

219 219 220 221 223 226 227 229 229 230 230 232 233 235 235 236

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Part IV: Signal Processing Myriad Filter Computation with 2nd Order Approximation Polynomial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tomasz Pander 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 The M-Estimator and the Myriad Filter . . . . . . . . . . . . . . . . . 3 Estimation of the Output Myriad Filter Using 2nd Order Approximation Polynomial . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Filtering Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Results of Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Electrophysiology-Based Monitoring System for a Human in Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Joanna Jaworek, Eliasz Ka´ ntoch 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Monitoring Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Waves and Intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Mean Electrical Axis . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Respiration Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Oxygen Saturation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 System Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Hardware Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Connection Modes and Data Flow . . . . . . . . . . . . . . 3.3 Data Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Experimental Database . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Future Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Analysis of Major Adverse Cardiac Events with Entropy-Based Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tuan D. Pham, Cuong C. To, Honghui Wang, Xiaobo Zhou 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Geostatistical Entropy (GeoEn) . . . . . . . . . . . . . . . . . . . . . . . . 3 Analysis of Major Adverse Cardiac Events . . . . . . . . . . . . . . . 3.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

239 239 241 242 245 248 248 249 251 251 252 252 253 253 255 255 255 256 257 258 259 259 259 260 261 261 263 265 265 266 270 271

Contents

Adaptive Time-Varying Frequency Characteristic Filtering of ECG Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Alina Momot, Michal Momot 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Adaptive Filtering Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Numerical Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Heart Rate Analysis in the EGG Examination . . . . . . . . . . . . . . . Stanislaw Pietraszek, Dariusz Komorowski 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 The EGG Preprocessing . . . . . . . . . . . . . . . . . . . . . . . 2.2 The ECG Preprocessing . . . . . . . . . . . . . . . . . . . . . . . 2.3 Calculation of Power Spectrum Density . . . . . . . . . . 2.4 Calculation of Dominant Frequency for Segments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Calculation of LF/HF Balance for Segments . . . . . . 3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Convergence Improving in Evolution–Based Technique for Estimation and Separation of Electrooculography and Blinking Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Robert Krupi´ nski, Przemyslaw Mazurek 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Model-Based Optimization Approach . . . . . . . . . . . . . . . . . . . 3 Improving Convergence by Initialization . . . . . . . . . . . . . . . . . 4 Results for Proposed Optimization Method . . . . . . . . . . . . . . 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

XVII

273 273 275 277 281 281 283 283 284 284 285 285 287 288 289 291 292

293 293 296 298 300 300 301

Part V: Bioinformatics Classification of DNA Microarray Data with Random Forests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tomasz Stokowy 1 Random Forests in Microarray Data Classification . . . . . . . . 2 Data Used in the Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Description of the Classification System . . . . . . . . . . . . . . . . . 4 Quality of Random Forests DNA Microarray Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Final Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

305 305 306 306 307 308 308

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Homogeneity Assessment of Cell Populations for High Content Screening Platforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Arkadiusz Gertych, Jian Tajbakhsh 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 HCS Platform Components . . . . . . . . . . . . . . . . . . . . 3.2 Image Preprocessing and Extraction of Intensity Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Pattern Similarity Analysis via Kullback-Leibler Divergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Homogeneity Assessment Based on Similarity Measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Conclusions and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Automated Cell Nuclei Segmentation in Breast Cancer Fine Needle Biopsy Smears . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Marek Kowal, Andrzej Obuchowicz 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Fuzzy Clustering with Shape Constraints . . . . . . . . . . . . . . . . 3 Cell Nuclei Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Model of Optical Sectioning by Using Structured Light in a Conventional Microscope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jan Juszczyk 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Principals of the Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Evaluation of Antibacterial Agents Activity . . . . . . . . . . . . . . . . . . Igor Buzalewicz, Katarzyna Wysocka-Kr´ ol, Katarzyna Kowal, Halina Podbielska 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Theoretical Concepts of Proposed Image Processing Analysis of Bacteria Colonies . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Antibacterial Efficiency Evaluated by Means of Optical Transforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . .

309 309 311 311 311 312 312 315 316 317 318 321 321 322 326 328 331 332 333 333 334 335 337 339 339 341

341 343 345 346

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XIX

3.2

The Evaluation of Antibacterial Agents Activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348 4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350 Part VI: Telemedicine Discrete Nonlinear Control of the Diagnostic Quality in Distributed Telemedical Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . Piotr Augustyniak 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Principles of Non-uniform Control . . . . . . . . . . . . . . . . . . . . . . 2.1 Components of the Control Loopback . . . . . . . . . . . 2.2 Static Properties and Control Accuracy . . . . . . . . . . 2.3 Automatic Scoring of the Procedure Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Dynamic Properties of the ECG Processing Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Experiments and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Prototype Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Static Accuracy of the Processing Optimization . . . 3.4 Dynamic Properties and Temporal Convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

355 355 356 357 358 360 361 362 362 363 363 364 364 366

Sleep Evaluation Device for Home-Care . . . . . . . . . . . . . . . . . . . . . Magdalena Smole´ n, Klaudia Czopek, Piotr Augustyniak 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Measurement Modalities and Methods . . . . . . . . . . . . . . . . . . 2.1 Analysis of Heart Rate Variability . . . . . . . . . . . . . . . 2.2 Analysis of Subject’s Motion . . . . . . . . . . . . . . . . . . . 2.3 Analysis of Acoustic Effects . . . . . . . . . . . . . . . . . . . . 3 System Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Software Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Conclusions and Future Works . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

367

A Graph Representation of Subject’s Time-State Space . . . . . . ´ Gra˙zyna Slusarczyk, Piotr Augustyniak 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Principles of the Surveillance System . . . . . . . . . . . . . . . . . . . 2.1 State and Behavior Observation . . . . . . . . . . . . . . . . 2.2 Qualification of the Behavior . . . . . . . . . . . . . . . . . . . 3 A Graph Representation of Subject’s Behavior . . . . . . . . . . .

379

367 368 369 370 371 373 376 377 378

379 380 381 383 384

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3.1 Definition of Subject’s State Graph . . . . . . . . . . . . . 3.2 A Graph Representation of Subject’s Habits . . . . . . 3.3 Quantifying of Behavior Differences . . . . . . . . . . . . . 4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Data Integration in Multimodal Home Care Surveillance and Communication System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Piotr Augustyniak, Magdalena Smole´ n, Anna Broniec, Jacek Chodak 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Electrical Activity of the Heart . . . . . . . . . . . . . . . . . 2.2 Mechanical Activity of the Body . . . . . . . . . . . . . . . . 2.3 Electrical Activity of the Brain as Status Determinant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Subject’s Motion Assessment and Emergency Detection in Context of the Localization . . . . . . . . . 2.5 Voluntary Activity of the Brain as Command Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Voluntary Eye Movements as Command Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Open Standards as a Basis of the Information Services Platform in Health Care Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kazimierz Fraczkowski, Michal Szczepaniak  1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Tendencies in the Development of System Integrations and Operability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Open Standards – Information Exchange Format XML . . . . 4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

384 385 386 388 389 391 391 392 393 394 395 396 397 398 401 401 402 403 403 405 409 412 413

Part VII: Biomechanics Application of Motion Analysis Systems in the Designing of a Rehabilitation Device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Robert Michnik, Jacek Jurkoj´c, Zbigniew Paszenda, Andrzej Michnik, Michal Bachorz, Wieslaw Rycerski, Jan Janota 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

417

417 418 420 422 422

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XXI

Control System for a Limb Rehabilitation Robot . . . . . . . . . . . . Andrzej Michnik, Jacek Brandt, Zbigniew Szczurek, Michal Bachorz, Zbigniew Paszenda, Robert Michnik, Jacek Jurkoj´c 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Assumptions of the Control System . . . . . . . . . . . . . . . . . . . . . 3 Construction of the Robot Control System . . . . . . . . . . . . . . 4 Construction of the Measurement and Performance Node . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Verification of the Concept of a Rehabilitation Robot Control System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

423

Methodology of Examining Fracture Surfaces of Biomaterials by Means of Modelling and Multifractal Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sebastian Stach, Zygmunt Wrobel 1 Introduction to the Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Acquisition of Stereometric Data for the Material Investigated . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 The Minimal Spanning Tree Method – 3DMST . . . . . . . . . . 4 Multifractal Analysis of Fracture Surface Based on 3DMST . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Conclusions and Further Work . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ACL Rehabilitation Enhanced by 3D Modeling Software . . . . . Marek Kr´ otkiewicz, Krystian Wojtkiewicz, Radoslaw Kardas 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Traditional Approach towards Rehabilitation . . . . . . . . . . . . 3 ACL Rehabilitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 The Use of 3D Modeling Application in ACL Rehabilitation Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Computer Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Numerical Analysis of Spine Stabilizers on Lumbar Part of Spine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Marta Kiel, Jan Marciniak, Marcin Basiaga, Janusz Szewczenko 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Results of Analysis of Lumbar Spine Transpedicular Stabilizer System . . . . . . . . . . . . . . . .

423 424 425 426 428 429 430

431 431 432 434 435 437 438 439 439 440 441 442 445 446 446 447 447 448 451 451

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3.2

Results of Analysis of Lumbar Spine – Pate Stabilizer System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453 4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456 Numerical Analysis of Low Contact Plate Made of Alternative Metallic Biomaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . Marcin Kaczmarek 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Geometrical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Numerical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Tibia - Stainless Steel LCP System . . . . . . . . . . . . . . 3.2 Tibia - Ti-6Al-4V LCP System . . . . . . . . . . . . . . . . . 4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Metatarsal Osteotomy Using Double-Threaded Screws - Biomechanical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Anna Ziebowicz, Anita Kajzer, Wojciech Kajzer, Jan Marciniak 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Biomechanical Behaviour of Surgical Drills in Simulated Conditions of Drilling in a Bone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Marcin Basiaga, Zbigniew Paszenda, Janusz Szewczenko 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Geometrical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Numerical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Strength Analysis Results - Variant I . . . . . . . . . . . . 3.2 Strength Analysis Results - Variant II . . . . . . . . . . . 4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

457 457 458 458 459 459 460 460 461 463 464 465 465 466 468 471 472 473 473 474 474 475 475 476 476 477 480 480

FEM Analysis of Instruments Used in Root Canal Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483 Witold Walke, Zbigniew Paszenda, Piotr Winiarski 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483

Contents

XXIII

2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Specific Evaluation of Pelvic Radiograms and Hip BMD in Structural Scoliosis Reflectorica and Reactive Pain Conditions of the Backbone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Andrzej Dyszkiewicz, Pawel Pole´c, Damian Chachulski, Pawel Kepi´  nski, Jakub Zajdel 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Study Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Patients Studied . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Exclusion Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Scoliosis Angle Assessment . . . . . . . . . . . . . . . . . . . . . 2.2 Assessment of the Hip Column by Means of the DXA Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Assessment of the Reference Points in the Pelvis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Photoplanimetric Assessment of the Muscular Structure of the Back . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

484 486 489 490

491

491 496 496 497 498 498 498 499 501 502 504 504 506

Part VIII: Bronchoscopy The BRONCHOVID – Computer System Supporting Bronchoscopy Laboratory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mariusz Duplaga, Jaroslaw Bulat, Mikolaj Leszczuk, Miroslaw Socha, Piotr Romaniak, Pawel Turcza 1 The Rationale for Development of Next Generation Computer System for Bronchoscopy Support . . . . . . . . . . . . 1.1 The Role of Bronchoscopy in Respiratory Medicine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 The Evolution of User Needs in Relation to Computer Support for Bronchoscopy Procedures and Data Management . . . . . . . . . . . . . . . . . . . . . . . . 2 Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 System Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Hardware and Software Solution . . . . . . . . . . . . . . . . 3.2 Data Repository . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Real Time Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . .

511

511 512

513 514 514 516 517 518

XXIV

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3.4 Editor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Virtual Bronchoscopy . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Data Browser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Deployment, Results and Future Development . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3D Segmentation and Visualisation of Mediastinal Structures Adjacent to Tracheobronchial Tree from CT Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Andrzej Skalski, Miroslaw Socha, Mariusz Duplaga, Krzysztof Duda, Tomasz Zieli´ nski 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Segmentation of Mediastinal Structures Located in the Vicinity of the Tracheobronchial Tree . . . . . . . . . . . . . . . . . . . 2.1 Segmentation Method Based on Region Growing and Deformable Models . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Analysis of Segmentation Effectiveness . . . . . . . . . . . 3 Automatic Generation of the Navigation Path . . . . . . . . . . . 4 Visualisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Algorithms for Automatic Recognition of Non-informative Frames in Video Recordings of Bronchoscopic Procedures . . . Michal Grega, Mikolaj Leszczuk, Mariusz Duplaga, Rafal Fraczek 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Approaches to Detection of “Non-informative” Frames . . . . 2.1 Edge Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 MPEG-7 Descriptors . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 HSV Histogram and Neural Networks . . . . . . . . . . . 2.4 Discrete Cosine Transform Method . . . . . . . . . . . . . . 3 Evaluation and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Evaluation Environment . . . . . . . . . . . . . . . . . . . . . . . 3.2 Analysis of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Further Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Using MPEG-7 Descriptors and Scoring Model to Automatically Recognize Medical Events in the Record of Bronchoscopy Video . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lucjan Janowski, Mariusz Duplaga, Krzysztof Suwada 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 MPEG-7 and Collected Data . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 MPEG-7 Description . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Describing Bronchoscopy Videos Examinations . . .

519 519 521 521 522

523

523 525 526 527 529 531 532 533 535 535 538 538 539 540 541 542 542 542 544 544 545

547 547 549 549 550

Contents

3 4

Scoring Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Model Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Bleeding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Mucosal Pallor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Three Stage Method Assisting Endobronchial Tumor Mass Recognition in Bronchoscopy Images . . . . . . . . . . . . . . . . . . . . . . . . Artur Przelaskowski, Rafal Jozwiak 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Informative Frames in Videobronchoscopy . . . . . . . . 1.2 Computer Assistance of Bronchoscopy Diagnosis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Material and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Three Stage Method Description . . . . . . . . . . . . . . . . 3 Experiments and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Application of SIFT Image Analysis Method to Support Transbronchial Needle-Aspiration Biopsy . . . . . . . . . . . . . . . . . . . . Piotr Pawlik, Mariusz Duplaga 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Outline of the SIFT Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Modification and Implementation of the SIFT Method . . . . 4 Verification of the Quality of the Method on Sequences of Pictures Generated during Bronchoscopic Examination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Verification of Real-Time Calculation Capability of the Method in Longer Image Sequences (Films) . . . . . . . . . . . . . . 6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Analysis of Images of Bronchial Tree Ramifications for Summarization of Bronchoscopic Videos . . . . . . . . . . . . . . . . . . . . . Zbigniew Mikrut, Mariusz Duplaga 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Shape Descriptors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

XXV

550 553 555 555 557 558 559 559 560 561 563 563 567 569 569 571 571 574 575

576 578 581 581 583 583 584 584 585 586 586

XXVI

Contents

Prototype Software for Video Summary of Bronchoscopy Procedures with the Use of Mechanisms Designed to Identify, Index and Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mikolaj Leszczuk, Michal Grega 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 “Non-informative” Frames . . . . . . . . . . . . . . . . . . . . . . 2.2 Markers from Medical Treatment . . . . . . . . . . . . . . . 2.3 Frames Annotated by Medical Doctors as References of Pathologies . . . . . . . . . . . . . . . . . . . . . . 2.4 Trachea-Bronchial Tree Branching (Ramifications) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Automatically Discovered Pathologies . . . . . . . . . . . 3 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Implementation of Methods for Acquiring Inclusive/Exclusive Factors . . . . . . . . . . . . . . . . . . . . . 3.2 Implementation of Graphical User Interface . . . . . . 4 Conclusions and Further Work . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Perception Enhancement of Bronchoscopic Video . . . . . . . . . . . . Grzegorz Ostrek, Artur Przelaskowski, Mariusz Duplaga, Aleksandra Rutczy´ nska 1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Assessment of the Bronchoscopy Image . . . . . . . . . . . . . . . . . 2.1 Bronchoscopy with Image Magnification . . . . . . . . . 2.2 Narrow Band Imaging . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Autofluorescence Bronchoscopy . . . . . . . . . . . . . . . . . 2.4 Endobronchial Thermic Measurement . . . . . . . . . . . 2.5 Spectroscopic Techniques . . . . . . . . . . . . . . . . . . . . . . 2.6 Endoscopic Microscopy . . . . . . . . . . . . . . . . . . . . . . . . 3 Methods of Perception Enhancement . . . . . . . . . . . . . . . . . . . 3.1 Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Experimental Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

587 587 589 589 592 592 592 593 593 593 594 596 596 599

599 600 600 601 601 601 602 602 602 603 603 605 608 609

Contents

XXVII

Part IX: Magnetic Field Analysis of Magnetic Field Distribution and Mechanical Vibration of Magnetic Field Exciter under Different Voltage Supply . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tomasz Trawi´ nski, Marcin Szczygiel, Joanna Wyszkowska, Krzysztof Kluszczy´ nski 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Scope of the Work and Laboratory Equipment . . . . . . . . . . . 3 Mathematical Model Formulation of Field Exciter and Results of Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Measurement Results of Real Exciter . . . . . . . . . . . . . . . . . . . 5 Results of Vibration Measurement . . . . . . . . . . . . . . . . . . . . . . 6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

613

614 615 615 618 618 620 622

Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623

On a Hybrid Fuzzy Clustering Method Tomasz Przybyła, Janusz Jez˙ ewski, and Dawid Roj

Abstract. This paper presents a new hybrid fuzzy clustering method. In the proposed method, cluster prototypes are values that minimize the introduced generalized cost function. The proposed method can be considered as a generalization of fuzzy c–means (FCM) method as well as the fuzzy c–median (FCMed) clustering method. The generalization of the cluster cost function is made by applying the L p norm. The values that minimize the proposed cost function have been chosen as the cluster prototypes. The weighted myriad is a special case of the cluster prototype when the L p norm is the L2 norm. The cluster prototypes are the weighted meridians for the L1 norm. Artificial data set is used to demonstrate the performance of proposed method, and the obtained results are compared to the results from the FCM method.

1 Introduction Let us consider a set of objects O = {o1 , . . . , oN }. The object set consists of unlabeled data, i.e. labels are not assigned to objects. The goal of clustering is to find existing subsets in the O set. Objects from one group have a high degree of similarity, while they have a high degree of dissimilarity with objects from other groups. Subsets that are found among the objects of the O set are called clusters [1, 2]. In most cases, each oi object from the O object set is represented by an x vector in the s-dimensional space i.e. x ∈ IRs . The set X = {x1 , . . . , xN } is called the object Tomasz Przybyła Silesian University of Technology, Institute of Electronics, Akademicka Str 16, 44-101 Gliwice, Poland e-mail: [email protected] Janusz Je˙zewski · Dawid Roj Institute of Medical Technology and Equipment ITAM, Departament of Biomedical Informatics, Roosvelta Str 118, 41-800 Zabrze, Poland E. Pi˛etka and J. Kawa (Eds.): Information Technologies in Biomedicine, AISC 69, pp. 3–14. c Springer-Verlag Berlin Heidelberg 2010 springerlink.com 

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T. Przybyła, J. Je˙zewski, and D. Roj

data representation of O. In such a case, the l-th component of the k-th feature vector xk gives a measure of l-th feature (e.g. length of flower petal, age of car, weight) of the k-th object ok . One of the most popular clustering method is the fuzzy c–means (FCM) method. In this method, cluster prototypes are computed as the fuzzy means [2]. However, one of the most important inconvenience of the FCM method is its sensitivity to outliers i.e. there are feature vectors which component (or components) have quite different value compared to other feature vectors. There are many modifications for the limitation of the outliers influence. In the first modification, the L2 norm is replaced by the L1 norm and by the generalized L p norm [3]. Another approach has been proposed by Krishnapuram and Keller [4, 5]. This clustering approach is based on possibilistic theory instead on fuzzy theory. One of the most interesting modification has been proposed by Kersten. In this method the L2 norm is replaced by the L1 norm, and the cluster prototypes are computed as fuzzy medians [6]. The use of heavy tailed distribution to model the impulsive noise gives better results than the use of Gaussian distribution [7, 8, 9, 10]. One of the havy tailed distribution is the Cauchy distribution, where the location parameter is called (sample) myriad [11]. The fuzzy myriads have been used as the cluster prototypes in the fuzzy c–myriads (FCMyr) clustering method [12]. Another example of the heavy tailed distribution is the Meridian distribution proposed by Aysal and Berner [13]. The location parameter for the Meridian distribution is called (sample) meridian. In the adaptative fuzzy c–meridians (AFCMer) clustering method, the cluster prototypes were computed as fuzzy meridians [14]. The myriad is the maximum likelihood estimator of the location parameter for the Cauchy distribution, so is the meridian for the Meridian distribution. The form of cost function for sample meridian is very similar to the sample meridian cost function. The L2 norm is used for the myriad cost function, where for the meridian cost function, the L1 norm is used. In this paper, the generalized cost function is presented. In the proposed cost function, the L p norm is used. Assuming p = 2 the generalized cost function becomes the myriad cost function, while for p = 1 the proposed cost function becomes the meridian cost function. Such a generalized cost function is used to determine the cluster prototypes in proposed clustering algorithm. The paper is organized as follows. Section II gives the genaralized cost function. The proposed clustering algorithm is introduced in Section III. Section IV contains numerical examples. The last section contains some conclusions and ideas for future research.

2 Generalized Cost Function 2.1 Weighted Myriad The probability density function (PDF) of the Cauchy distribution is described in the following way

On a Hybrid Fuzzy Clustering Method

5

  K 1 f (x; Θ ) = , 2 π K + (x − Θ )2

(1)

where Θ is the location parameter, and K is the scaling factor (K > 0). The Figure 1 shows the PDF of the Cauchy distribution for scale parameter K = 1 and location Θ = 0 (solid line) and the PDF of the normal distribution N(0, 1) (dashed line). It can be noticed that the Cauchy distribution has heavier tails.

0.4

0.4

0.35

0.35

0.3

0.3

0.25

0.25

0.2

0.2

0.15

0.15

0.1

0.1

0.05

0.05

0 −5

0

5

0

0

(a)

5

10

15

(b)

Fig. 1 Cauchy (solid line) and Normal (dashed line) probability density functions

For the given set of N independent and identically distributed (i.i.d.) samples each obeying the Cauchy distribution with the common scale parameter K, the sample myriad Θˆ K is a value that minimizes the cost function ΨK defined as follows [15]

Θˆ K = arg min

  2 2 log K + (x − Θ ) k ∑ N

Θ ∈IR k=1

= arg min ΨK (x; Θ ) Θ ∈IR   =myriad xk |Nk=1 ; K

.

(2)

By assigning non–negative weights to the input samples, the weighted myriad Θˆ K is derived as a generalization of the sample myriad. For the N i.i.d. observations {xk }Nk=1 and the {uk }Nk=1 , the weighted myriad can be computed from the following expression

Θˆ K = arg min

N

∑ log

Θ ∈IR k=1

  K 2 + uk (xk − Θ )2

= arg min ΨK (x, u; Θ ) Θ ∈IR   =myriad uk ∗ xk |Nk=1 ; K

.

(3)

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T. Przybyła, J. Je˙zewski, and D. Roj

The value of weighted myriad depends on the data set x, the assigned weights u and the parameter K, called a linearity parameter. Two interesting cases may occur. First, when the K value tends to infinity (i.e. K → ∞), then the value of weighted myriad converges with the weighted mean, that is lim Θˆ K =

K→∞

∑Nk=1 uk xk , ∑Nk=1 uk

(4)

 N where Θˆ K = myriad uk ∗ xk |Nk=1 ; K k=1 . This property is called myriad linear property [11, 15]. Second case, called modal property, occurs when the value of K parameter tends to zero (i.e. K → 0). In this case the value of the weighted myriad is always equal to one of most frequent values in the input data set, i.e.:

Θˆ 0 = arg min x j ∈Ξ

where

N

∏

k=1,xk =x j

  xk − x j  ,

(5)

Θˆ 0 = lim Θˆ K , K→0

and Ξ is a set that contains the most frequent data in the input data set x. The value Θˆ K is defined in the same way as in the linear property. For the data set x = {0.13, 0.16, 0.27, 0.39, 0.86, 0.90, 0.95, 0.97, 0.99} and the assigned weights u = {0.70, 0.60, 0.39, 0.94, 0.26, 0.02, 0.04, 0.08, 0.05}, the example of possible shapes of the weighted myriad cost function (3) are presented in Figure 2.

2.2 Weighted Meridian The random variable formed as the ratio of two independent zero–mean Laplacian distributed random variables is refered to as the Meridian distribution. The Meridian distribution has been proposed by Aysal and Berner [13]. The form of the proposed distribution is given by   δ 1 f (x; δ ) = . (6) 2 (δ + |x|)2 The standard Cauchy and Meridian PDFs are plotted in Figure 3 , where K = δ = 1. It can be seen that the Meridian distribution has heavier tails than the Cauchy distribution. For the given set of N i.i.d. samples {xk }Nk=1 each obeying the Meridian distribution with the common scale parameter δ , the sample meridian βˆδ is given by [13]

On a Hybrid Fuzzy Clustering Method

7

−10

−12 K=0.1 −14

ΨK(Θ)

K=0.05 −16

K=0.001

−18

−20

−22

−24

0

0.2

0.4

0.6

Θ

0.8

1

Fig. 2 An illustration of the shape of weighted myriad cost function 0.5

0.05

0.45

0.045

0.4

0.04

0.35

0.035

0.3

0.03

0.25

0.025

0.2

0.02

0.15

0.015

0.1

0.01

0.05

0.005

0 −5

0

0

5

0

5

10

(a)

15

(b)

Fig. 3 The Meridian distribution (solid line) and the Cauchy (dashed line) distribution

βˆδ = arg min

N

∑ log [δ + |xk − β |]

β ∈IR k=1

= arg min φδ (x; β ) β ∈IR   =meridian xk |Nk=1 ; δ

,

(7)

where Φδ is the sample meridian cost function. Parameter δ is called the medianity parameter. The sample meridian βˆδ is the ML estimator of the location parameter for the Meridian distribution. The sample meridian can be generalized to the weighted

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T. Przybyła, J. Je˙zewski, and D. Roj

meridian by assigning non–negative weights to the input samples. So, the weighted meridian is given by

βˆδ = arg min

N

∑ log [δ + uk|xk − β |]

β ∈IR k=1

= arg min φδ (x, u; β ) β ∈IR   =meridian uk ∗ xk |Nk=1 ; δ

.

(8)

The behavior of the weighted meridian significantly depends on the value of its medianity parameter δ . Two interesting cases may occur. The first case occurs when the value of the medianity parameter tends to infinity (i.e. δ → ∞), the the weighted meridian is equivalent to the weighted median [13]. For the given data set of N i.i.d. samples x1 , · · · , xN and assigned weights u1 , · · · , uN , the following equation holds true     lim βˆδ = lim meridian uk ∗ xk |Nk=1 ; δ = median uk ∗ xk |Nk=1 . (9) δ →∞

δ →∞

This property is called the median property. The second interesting case, called the modal property, occurs when the medianity parameter δ tends to zero. In this case, the weighted meridian βˆδ is equal to one of the most repeated values in the input data set. Furthermore

N 1 lim βˆδ = arg min (10) ∏ uk |xk − x j | , x j ∈Xi urj δ →0 k=1,x =x j k

where Xi is the set of the frequently repeated values, and r is the number of occurrences of a member of Xi in the sample set. Like for the weighted myriad cost function example, the Figure 4 shows shapes of the weighted meridian cost function for different values of δ parameter.

2.3 Generalized Cost Function Comparing the properties of the weighted myriad cost function and weighted meridian cost function common features can be found. One of them is the behavior of the both cost function when the K parameter and the δ parameter tend to zero. Then, for the same data set X, the value of weighted myriad is equal to the value of the weighed meridian. Another common feature of both functions is their similar form, but the weighted myriad cost function uses the L2 norm while the weighted meridian cost function uses the L1 norm. Let the L p norm be defined as follows

On a Hybrid Fuzzy Clustering Method

9

−5 −6 δ=0.1 −7

Φδ(β)

−8

δ=0.05

−9 −10 −11

δ=0.001

−12 −13 −14 0

0.2

0.4

β

0.6

0.8

1

Fig. 4 An illustration of the shapes of weighted meridian cost function for the sample data and different values of the medianity parameter δ

 ||z|| p =

s

∑ |zl | p

1p ,

(11)

l=1

where z is an s–dimensional real vector (i.e. z ∈ IRs ). Applying the L p norm to the weighted myriad cost function (3) or weighted meridian cost function (8), the generalized cost function can be expressed in the following form (p)

χγ (ν ) =

N

∑ log [γ + uk||xk − ν || p]

,

(12)

k=1

where ||·|| p is the L p norm to the p power, and parameter γ corresponds to medianity parameter δ for p = 1 and corresponds to linearity parameter K for p = 2. It should be mentioned, that for p = 1 the γ parameter is equal to medianity parameter δ , but for p√= 2 parameter γ is equal to the square root of the linearity parameter K (i.e. γ = K). For the given data set {xk }Nk=1 and the assigned weights {uk }Nk=1 , let the νˆ γ be the value minimizing the cost function (12), i.e. (p) νˆ γ = arg min χγ (ν )

ν ∈IR

N

= arg min

ν ∈IR

∑ log [γ + uk ||xk − ν || p]

k=1

.

(13)

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T. Przybyła, J. Je˙zewski, and D. Roj

Properties of the νˆ γ value are presented in Table 1. Table 1 Properties of the νˆ γ estimator

γ γ →0 0<γ <∞

p=1 p=2 most repeated values in the input data set √ N νˆ γ = meridian(uk ∗ xk |N k=1 ; γ ) νˆ γ = myriad(uk ∗ xk |k=1 ; γ )

γ →∞

νˆ γ = median(uk ∗ xk |N k=1 )

νˆ γ = mean(uk ∗ xk |N k=1 ) =

∑Nk=1 uk xk ∑Nk=1 uk

(p)

The function χγ (ν ) can be regarded as a generalized cost function. For p = 1 a weighted meridian is a special case of νˆ γ , and for p = 2 the weighted myriad is a special case of νˆ γ . Assuming without loss of generality that the weights are in the unit interval (i.e. uk ∈ [0, 1] where 1 ≤ k ≤ N), the weights can be interpreted as membership degrees. Then, a weighted myriad Θˆ K or a weighted meridian βˆδ can be interpreted as a fuzzy myriad or fuzzy meridian, respectively. In the rest of this paper, the weights will be treated as a membership degrees and the weighted myriad and weighted meridian will be interpreted as fuzzy myriad and fuzzy meridian. Also, the νˆ γ value will be interpreted as a fuzzy value.

3 Hybrid Clustering Method Let us consider a clustering category in which partitions of data set are built on the basis of some performance index, known also as an objective function [2, 16]. The minimization of a certain objective function can be considered as an optimization approach leading to suboptimal configuration of the clusters. The main design challenge is formulating an objective function that is capable of reflecting the nature of the problem so that its minimization reveals a meaningful structure in the data set. The partition of an input data set can be described by c × N matrix (where c is the number of clusters, and N is the number of data samples), called the partition matrix. For the fuzzy clustering methods, the fuzzy partition matrix is defined as follows

 U ∈ [0, 1]c×N | M fCN = . (14) ∑ci=1 uik = 1, 1 ≤ k ≤ N; ∑Nk=1 uik > 0, 1 ≤ i ≤ c The proposed method is an objective functional based on fuzzy c–partitions of the finite data set [2, 16]. The suggested objective function can be an extension of the classical functional of within–group sum of an absolute error. The objective function of the chosen method can be described in the following way

On a Hybrid Fuzzy Clustering Method c

Jm (U, V) = ∑ (p)

11

N

s

∑ ∑ log [γ + umik||xk (l) − vi (l)|| p ]

,

(15)

i=1 k=1 l=1

where c is the number of clusters, N is the number of the data samples, s is the number of features describing the clustered objects. The γ parameter controls the behavior of cluster prototypes, uik ∈ U is the membership degree of the k–sample to the i–th cluster, the U is the fuzzy partition matrix, xk (l) represents the l–th feature of the k–th input data from the data set, and m is the fuzzyfing exponent called the fuzzyfier. (p) The optimization objective function Jm is completed with respect to the partition matrix U and the prototypes of the clusters V. By minimizing (15) using Lagrangian multipliers, the following new membership uik update equation    c ||xk − vi|| p 1/(m−1) uik = ∑ , (16) j=1 ||xk − v j || p can be derived. For the case, where ||xk − vi || p = 0, then uik = 1 and u jk = 0 for j ∈ {1 · · · c} − {i}. For the fixed number of clusters c and the partition matrix U as well as for the exponent m, the prototype values minimizing (15) are the values described as follows N

vi (l) = arg min

ν ∈IR

∑ log [γ + umik||xk (l) − ν || p]

,

(17)

k=1

where i is the cluster number 1 ≤ i ≤ c and l is the component (feature) number 1 ≤ l ≤ s.

3.1 Data Clustering with the Hybrid Clustering Method The proposed hybrid clustering method can be described as follows: 1. For the given data set X = {x1 , · · · , xN } where xi ∈ IRs , fix the number of clusters c ∈ {2, · · · , N}, the fuzzyfing exponent m ∈ [1, ∞) and assume the tolerance limit ε . Initialize randomly the partition matrix U and fix the value of parameter γ , fix l = 0, 2. calculate the prototype values V for each feature of vi based on (17), 3. update  the partition  matrix U using (16),  (l+1) (l)  4. if U − U  < ε then STOP the clustering algorithm, otherwise l = l + 1 and go to (2).

12

T. Przybyła, J. Je˙zewski, and D. Roj

4 Numerical Experiments In the numerical experiments the fuzzfing exponent has been fixed to m = 2, and the tolerance limit ε = 10−5 . For a computed set of prototype vectors V the clustering accuracy has been measured as the Frobenius norm distance between the true centers μ and the prototype vectors. The matrix A is created as ||μ − V||F , where ||A||F : 1/2

 ||A||F =

∑

.

A2i,k

i,k

The familiar fuzzy c–means method (FCM) has been used as the reference clustering method. The purpose of this experiment is to investigate sensitivity to outliers of the proposed method. The left column of the table 2 gives the number of outliers included in the data set. The Figure 5 shows the data of 42 samples, used in the numerical experiment. The data set consists of well–separated two radial clusters centered at μ1 = [0.3 0.3] and μ2 = [0.8 0.3] . Moreover, in the data set at o = [10.0 10.0] the various number of outliers have been placed. The purpose of this experiment is to investigate sensitivity to outliers. The obtained results are presented in the Table 2.

1 0.9 0.8 0.7

x

2

0.6 0.5 0.4 0.3 0.2 0.1 0

0

0.2

0.4

0.6

0.8

1

x

1

Fig. 5 “Two cluster data” scatterplot

For the number of 20 outliers, there was no deterioration in the quality of clustering for small values of parameter γ (i.e. γ ≤ 0.1). The small value of parameter

On a Hybrid Fuzzy Clustering Method

13

Table 2 The difference among computed cluster centers V and the true centers μ

outliers 0 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20

100 0.0321 13.1382 13.2558 13.2945 13.3139 13.3253 13.3331 13.3385 13.3426 13.3458 13.3484 13.3522 13.3550 13.3570 13.3586 13.3599

10 0.0321 13.1382 13.2558 13.2945 13.3139 13.3253 13.3331 13.3385 13.3426 13.3458 13.3484 13.3522 13.3550 13.3570 13.3586 13.3599

p=2 γ 1 0.0321 0.0338 0.0384 0.0453 0.0534 0.0625 0.0722 0.0823 0.0926 0.1033 0.1140 0.1363 0.1595 0.1834 0.2091 0.2351

p=1 γ 0.1 0.01 100 10 1 0.0297 0.0008 0 0 0 0.0297 0.0008 0 0 0 0.0297 0.0008 0 0 0 0.0297 0.0008 0 0 0 0.0297 0.0008 0 0 0 0.0297 0.0008 0 0 0 0.0297 0.0008 0 0 0 0.0297 0.0008 0 0 0 0.0298 0.0008 0 0 0 0.0297 0.0008 0 0 0 0.0298 0.0008 0 0 0 0.0298 0.0008 0 0 0 0.0298 0.0008 0 0 0 0.0298 0.0008 0.4031 0.4031 0 0.0299 0.0008 0.4031 0.4528 0 0.0300 0.0008 0.1658 0.4528 0

FCM 0.1 0.01 0 0 0.0018 0 0 13.3712 0 0 13.3713 0 0 13.3713 0 0 13.3713 0 0 13.3713 0 0 13.3713 0 0 13.3713 0 0 13.3713 0 0 13.3713 0 0 13.3713 0 0 13.3713 0 0 13.3713 0 0 13.3713 0 0 13.3713 0 0 13.3713

γ affects the selectivity of the determination of the cluster prototypes. For the value of parameter γ = 0.01, the assumed norm does not influence on the quality of clustering. For the L2 norm and the values of parameter γ ≥ 10, the obtained clustering results are almost identical with those obtained by the FCM method. It shows that the proposed method can be regarded as a generalization of the FCM method. For the L1 norm, the obtained results are generally better than the results obtained for the L2 norm for the same values of parameter γ . This feature arises from the fact, that the proposed method can also be regarded as the generalization of the fuzzy c–median method, which is more robust than the fuzzy c–means method. The fuzzy c–means method dramatically breaks down for one outlier.

5 Conclusions In many cases, the real data are corrupted by noise and outliers. Hence, the clustering methods should be robust for noise and outliers. In this paper the hybrid clustering method has been presented. The word hybrid stands for different cluster estimation which is dependent on two parameters. The proposed method can be treated as a generalization of two clustering methods: the fuzzy c–means method and the fuzzy c–medians method. The presented generalization of the cost function allows the application of the L p norm, where 1 < p < 2 or p < 1. In such cases, it is difficult to interpret and identify the value νˆ .

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The current work solves the local minima problem and the performance of the cluster centers estimation for large data sets. Acknowledgements. This work was partially supported by the Ministry of Science and Higher Education resources in 2007–2010 under Research Project R1302802.

References 1. Kaufman, L., Rousseeuw, P.: Finding Groups in Data. Wiley–Interscience, Chichester (1990) 2. Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum, New York (1981) 3. Hathaway, R.J., Bezdek, J.C., Hu, Y.: Genalized Fuzzy c-Means Clustering Strategies Using L p Norm Distances. IEEE Trans. on Fuzzy Sys. 8, 576–582 (2000) 4. Krishnapuram, R., Keller, J.M.: A Possibilistic Approach to Clustering. IEEE Trans. on Fuzzy Sys. 1, 98–110 (1993) 5. Krishnapuram, R., Keller, J.M.: The Possibilistic C–Means Algorithm: Insights and Recomendations. IEEE Trans. on Fuzzy Sys. 4, 385–396 (1996) 6. Kersten, P.R.: Fuzzy Order Statistics and Their Application to Fuzzy Clustering. IEEE Trans. on Fuzzy Sys. 7, 708–712 (1999) 7. Huber, P.: Robust statistics. Wiley, New York (1981) 8. Dave, R.N., Krishnapuram, R.: Robust Clustering Methods: A Unified View. IEEE Trans. on Fuzzy System 5, 270–293 (1997) 9. Chatzis, S., Varvarigou, T.: Robust Fuzzy Clustering Using Mixtures of Student’s–t Distributions. Pattern Recognition Letters 29, 1901–1905 (2008) 10. Frigui, H., Krishnapuram, R.: A Robust Competitive Clustering Algorithm With Applications in Computer Vision. IEEE Trans. Pattern Analysis and Machine Intelligence 21, 450–465 (1999) 11. Arce, G.R., Kalluri, S.: Fast Algorithm For Weighted Myriad Computation by Fixed Point Search. IEEE Trans. on Signal Proc. 48, 159–171 (2000) 12. Przybyła, T.: Fuzzy c–Myriad Clustering Method, System Modeling Control, pp. 249– 254 (2005) 13. Aysal, T.C., Barner, K.E.: Meridian Filtering for Robust Signal Processing. IEEE Trans. on Signal Proc. 55, 3949–3962 (2007) 14. Przybyła, T., Je˙zewski, J., Horoba, K.: The Adaptive Fuzzy Meridian and Its Application to Fuzzy Clustering. In: Advances in Intelligent and Soft Computing, vol. 57, pp. 247– 256. Springer, Heidelberg (2009) 15. Arce, G.R., Kalluri, S.: Robust Frequency–Selective Filtering Using Weighted Myriad Filters admitting Real–Valued Weights. IEEE Trans. on Signal Proc. 49, 2721–2733 (2001) 16. Pedrycz, W.: Konwledge–Based Clustering. Wiley Interscience, Chichester (2005)

Complete Gradient Clustering Algorithm for Features Analysis of X-Ray Images Małgorzata Charytanowicz, Jerzy Niewczas, Piotr Kulczycki, Piotr A. Kowalski, ˙ Szymon Łukasik, and Sławomir Zak

Abstract. Methods based on kernel density estimation have been successfully applied for various data mining tasks. Their natural interpretation together with suitable properties make them an attractive tool among others in clustering problems. In this paper, the Complete Gradient Clustering Algorithm has been used to investigate a real data set of grains. The wheat varieties, Kama, Rosa and Canadian, characterized by measurements of main grain geometric features obtained by X-ray technique, have been analyzed. The proposed algorithm is expected to be an effective tool for recognizing wheat varieties. A comparison between the clustering results obtained from this method and the classical k-means clustering algorithm shows positive practical features of the Complete Gradient Clustering Algorithm.

1 Introduction Clustering is a major technique for data mining, used mostly as an unsupervised learning method. The main aim of cluster analysis is to partition a given population into groups or clusters with common characteristics, since similar objects are Małgorzata Charytanowicz · Jerzy Niewczas Institute of Mathematics and Computer Science, The John Paul II Catholic University of Lublin, Konstantynów 1 H, PL 20-708 Lublin, Poland e-mail: {mchmat,jniewczas}@kul.lublin.pl Piotr Kulczycki Department of Automatic Control and Information Technology, Cracow University of Technology, Warszawska 24, PL 31-155 Cracow, Poland e-mail: [email protected] ˙ Piotr A. Kowalski · Szymon Łukasik · Sławomir Zak Systems Research Institute, Polish Academy of Sciences, Newelska 6, PL 01-447 Warsaw, Poland e-mail: {pakowal,slukasik,slzak}@ibspan.waw.pl E. Pi˛etka and J. Kawa (Eds.): Information Technologies in Biomedicine, AISC 69, pp. 15–24. c Springer-Verlag Berlin Heidelberg 2010 springerlink.com 

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grouped together, while dissimilar objects belong to different clusters [9, 12]. As a result, a new set of categories of interest, characterizing the population, is discovered. The clustering methods are generally divided into six groups: hierarchical, partitioning, density-based, grid-based, and soft-computing methods. These numerous concepts of clustering are implied by different techniques of determination of the similarity and dissimilarity between objects. A classical partitioning k-means algorithm is concentrated on measuring and comparing the distances among them. It is computationally attractive and easy to interpret and implement in comparison to other methods. On the other hand, the number of clusters is assumed here by user in advance and therefore the nature of the obtained groups may be unreliable for the nature of the data, usually unknown before processing. The rigidity of arbitrary assumptions concerning the number or shape of clusters among data can be overcome by density-based methods that let the data detect inherent data structures. In the paper [8], the Complete Gradient Clustering Algorithm was introduced. The main idea of this algorithm assumes that each cluster is identified by local maxima of the kernel density estimator of the data distribution. The procedure does not need any assumptions concerning the data and may be applied to a wide range of topics and areas of cluster analysis [3, 8]. The main purpose of this work is to propose an effective technique for forming proper categories of wheat. In the earliest attempts to classify wheat grains a geometry and set of parameters were defined. The size, shape and colour of grain because of their heritable characters, can be used for wheat variety recognition. Accomplished studies showed that digital image processing techniques commonly used in multivariate analysis give reliable results in classification process [11, 14, 16]. In this paper, the algorithm proposed in [8] will be used to identify wheat varieties, using their main geometric features.

2 Complete Gradient Clustering Algorithm (CGCA) In this section, the Complete Gradient Clustering Algorithm, for short the CGCA, is shortly described. The principle of the proposed algorithm is based on the distribution of the data; the implementation of the CGCA needs to estimate its density. Each cluster is characterized by a local maximum of the kernel density estimator. As a result, regions of high densities of objects are recognized as clusters, while areas with sparse distributions of objects divide one group from another. Data points are assigned to clusters by using an ascending gradient method, i.e. points moving to the same local maximum are put into the same cluster. The algorithm works in an iterative manner until a termination criterion has been satisfied.

2.1 Kernel Density Estimation Suppose that x1 , x2 , . . . , xm is a random sample of m points in n-dimensional space from an unknown distribution with density f . Its kernel estimator can be defined as

Complete Gradient Clustering Algorithm for Features Analysis of X-Ray Images

1 m fˆ(x) = ∑K mhn i=1



 x − xi , h

17

(1)

where the positive coefficient h is called the smoothing parameter or bandwidth,  while the measurable function K : Rn → [0, ∞) of unit integral Rn K(x)dx = 1, unimodal and symmetrical with respect to zero, takes the name of a kernel [4, 13]. It is generally accepted, that the choice of the kernel K is not as important as the choice of the coefficient h and thank to this, it is possible to take into account the primarily properties of the estimator obtained. Most often the standard normal kernel given by xT x 1 K(x) = n/2 e− 2 (2) 2π is used. It is differentiable up to any order and assumes positive values in the whole domain. The practical implementation of the kernel density estimators requires a proper choice of the bandwidth h. The best value of h is mostly taken as the value that minimizes the mean integrated square error. A frequently used bandwidth selection method is based on the approach of least-squares cross validation [4, 13]. The value of h is chosen to minimize the function M : (0, ∞) → R given by the rule:   1 m m  x j − xi 2 M(h) = 2 n ∑ ∑ K + n K(0), (3) m h i=1 j=1 h mh  = K ∗2 (x) − 2K(x) and K ∗2 is the convolution square of the function K; where K(x) for the standard normal kernel (2): K ∗2 (x) =

1

e− (4π )n/2

xT x 4

.

(4)

In this case the influence of the smoothing parameter on particular kernels is the same. The individualization of this effect may be achieved through the modification of the smoothing parameter. This relies on introducing the positive modifying parameters s1 , s2 , . . . , sm mapped on particular kernels, described by the formula  si =

fˆ∗ (xi ) s

−c ,

(5)

where c ∈ [0, ∞), fˆ∗ is the kernel estimator in its basic form (1) and s denotes the geometrical mean of the numbers fˆ∗ (x1 ), fˆ∗ (x2 ), . . ., fˆ∗ (xm ). The value of the parameter c implies the intensity of modification of the smoothing parameter. Based on indications for the criterion of the mean integrated square error the value 0.5 as c is proposed. Finally, the kernel estimator with modification of the smoothing parameter is defined as

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1 m 1 fˆ(x) = ∑ sn K mhn i=1 i



 x − xi . hsi

(6)

Additional procedures improving the quality of the estimator obtained, such as a linear transformation and support boundary, as well as the general aspects of the theory of statistical kernel estimators are found in [4, 5, 13]. Exemplary practical applications are presented in the publications [1, 3, 6, 7].

2.2 Procedures of the CGCA Consider the data set containing m elements x1 , x2 , . . . , xm in n-dimensional space. Using the methodology introduced in Subsect. 2.1, the kernel density estimator fˆ may be constructed. The idea of the CGCA is based on the approach proposed by Fukunaga and Hostetler [2]. Thus given the start points: x0j = x j for j = 1, 2, . . . , m,

(7)

each point is moved in an uphill gradient direction using the following iterative formula: xk+1 = xkj + b j

∇ fˆ(xkj ) for j = 1, 2, . . . , m and k = 0, 1, . . . , fˆ(xk )

(8)

j

where ∇ fˆ denotes the gradient of kernel estimator fˆ, the value of the parameter b is proposed as h2 /(n + 2) and the coefficient h is the bandwidth of fˆ. The algorithm will be stopped when the following condition is fulfilled: |Dk − Dk−1 | ≤ α D0 ,

(9)

where D0 and Dk−1 , Dk denote sums of Euclidean distances between particular elements of the set x1 , x2 , . . . , xm before starting the algorithm as well as after the (k − 1)-th and k-th step, respectively. The positive parameter α is taken arbitrary and the value 0.001 is primarily recommended. This k-th step is the last one and will be denoted hereinafter by k∗ . Finally, after the k∗ -th step of the algorithm (7)-(8) the set ∗

∗

∗

xk1 , xk2 , . . . , xkm ,

(10)

considered as the new representation of all points x1 , x2 , . . . , xm , is obtained. Following this, the set of mutual Euclidean distances of the above elements:   ∗ ∗ d(xki , xkj ) i=1,2,...,m−1 (11) j=i+1,i+2,...,m

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19

is defined. Using the methodology presented in Subsect. 2.1, the auxiliary kernel estimator fˆd of the elements of the set (11), treated as a sample of a one-dimensional random variable, is created under the assumption of nonnegative support. Next, the first (i.e. obtained for the smallest value of an argument) local minimum of the function fˆd belonging to the interval (0, D), where D means the maximum value of the set (11) is found. This local minimum will be denoted as xd , and it can be interpreted as the half-distance between potential closest clusters. Finally, the clusters are created. First, the element of the set (11) is taken; it initially creates a one-element cluster containing it. An element of the set (11) is added to the cluster if the distance between it and any element belonging to the cluster is less than xd . Every added element is removed from the set (11). If there are no more elements belonging to the cluster, the new cluster is created. The procedure of assigning elements to clusters is repeated as long as the set (11) is not empty. Procedures described above constitute the Complete Gradient Algorithm in its basic form. The values of the parameters used are calculated automatically, using optimization criteria. However, by an appropriate change in values of these parameters it is possible to influence the size of number of clusters, and also the proportion of their appearnce in dense areas in relation to sparse regions of elements in this set. Namely, lowering (raising) the value of smoothing parameter h results in raising (lowering) the number of local maxima. A change in the value of that parameter of between -25% and +50% is recommended. Next, raising the intensity c of the smoothing parameter modification results in decreasing the number of clusters in sparse areas of data and increasing their number in dense regions. Inverse effects can be seen in the case of lowering this parameter value. The value of the parameter c to be between 0 and 1.5 is recommended. Finally, an increase of both parameters c and h can be proposed. Then the additional formula h∗ =

 c−0.5 3 h 2

(12)

is used for calculating the smoothing parameter h∗ , where the value of the parameter h is calculated on the criterion of the mean integrated square error. The joint action of both these factors results in a twofold smoothing of the function fˆ in the regions where the elements of the set x1 , x2 , . . . , xm are sparse. Meanwhile these factors more or less compensate for each other in dense areas, thereby having small influence on the detection of clusters located there. Detailed information on the CGCA procedures and their influences on the clustering results is described in [8].

3 Materials and Methods The proposed algorithm has been applied for wheat variety recognition. Studies were conducted using combine harvested wheat grain originating from experimental fields, explored at the Institute of Agrophysics of the Polish Academy of Sciences

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in Lublin. The examined group comprised kernels belonging to three different varieties of wheat: Kama, Rosa and Canadian, 70 elements each, randomly selected for the experiment. High quality visualization of the internal kernel structure was detected using a soft X-ray technique. It is non-destructive and considerably cheaper than other more sophisticated imaging techniques like scanning microscopy or laser technology. The images were recorded on 13 × 18 cm X-ray KODAK plates. Figure 1 presents the X-ray images of these kernels.

Fig. 1 X-ray photogram (13 × 18 cm) of kernels

The X-ray photograms were scanned using the Epson Perfection V700 table photo-scanner with a built-in transparency adapter, 600 dpi resolution and 8 bit gray scale levels. Analysis procedures of obtained bitmap graphics files were based on the computer software package GRAINS, specially developed for X-ray diagnostic of wheat kernels [10, 15]. To construct the data, seven geometric parameters of wheat kernels: area A, perimeter P, compactness C = 4π A/P2 , length of kernel, width of kernel, asymmetry coefficient and length of kernel groove, were measured from a total of 210 samples (see Fig. 2). All of these parameters were real-valued continuous. In our investigations, the data was reduced to be two-dimensional after applying the Principal Component Analysis [12] to validate the results visually.

4 Results and Discussion The data’s projection on the axes of the two greatest principal components, with wheat varieties being distinguished symbolically, is presented in Fig. 3. Samples were labeled by numbers: 1-70 for the Kama wheat variety, 71-140 for the Rosa wheat variety, and 141-210 for the Canadian wheat variety. To discuss the clustering

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21

Fig. 2 Document window with geometric parameters of a kernel and statistical parameters of its image (as a unit of measure millimeters were used)

results obtained by the CGCA, mistakenly classified samples are displayed with their labels (see Fig. 3). Using procedures described in Subsect. 2.2 allowing elimination of clusters in sparse areas, the CGCA created three clusters corresponding to Rosa, Kama, and Canadian varieties, containing 69, 65, and 76 elements respectively. Thus, the samples 9 and 38, which belong to the Kama wheat variety are incorrectly grouped into the cluster associated with the Rosa wheat variety. What is more, the samples 125, 136, 139, which belong to the Rosa wheat variety, and the samples 166, 200, 202, which belong to the Canadian wheat variety are mistakenly classified into the cluster associated with the Kama wheat variety. In addition, the samples 20, 27, 28, 30, 40, 60, 61, 64, 70, which belong to the Kama wheat variety are mistakenly classified into the cluster associated with the Canadian wheat variety. It is worth noticing however, that in the case of samples 9 and 38, misclassification can be justifiable – both samples lie close to the area of a high density of the Rosa wheat variety samples. The same problem is discerned with samples 125, 136, 139 and 166, 200, 202, which are placed close to samples of the Kama wheat variety. Similarly, mistakenly classified samples 20, 27, 28, 30, 40, 60, 61, 64, 70 lie very close to samples of the Canadian wheat variety. Thus, taking into consideration characteristics of wheat varieties, the CGCA seems to be an effective technique for wheat variety recognition. Clustering results, containing numbers of samples classified properly and mistakenly into clusters associated with Rosa, Kama and Canadian varieties, are shown in Table 1. According to the results of the CGCA, out of 70 kernels of the Rosa wheat variety, 67 were classified properly. Only 2 of the Kama variety were classified mistakenly as

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2

1 40 139

70

0

64

30

9

20 27 28

136

-1 61

38

60

125

166 200

-2

-3

202

-4

-3

-2

-1

0

1

2

3

4

5

Fig. 3 Wheat varieties data set on the axes of the two greatest principal components: (◦) the Rosa wheat variety, (×) the Kama wheat variety, ( ) the Canadian wheat variety Table 1 Clustering results for the wheat varieties data set Number of elements in clusters Clusters

Correctly classified

Incorrectly classified Total

Rosa Kama Canadian

67 59 67

2 6 9

69 65 76

the Rosa variety. For the other two varieties, the CGCA created clusters containing 65 elements (the Kama variety) and 76 elements (the Canadian variety). In regard to the Kama variety, 59 kernels were classified correctly, while 6 of the other varieties were incorrectly identified as the Kama variety. For the Canadian variety, 67 kernels were correctly identified and 9 kernels of the Kama variety were mistakenly identified as the Canadian variety. The results of Kama and Canadian varieties are not so satisfactory as for Rosa, and this implies that these two varieties could not be so clearly distinguished as the Rosa variety, when using main geometric parameters. It is worth underlining that the proper number of clusters has also been obtained when only two varieties are chosen to examine the CGCA. Thus, for Kama and Canadian varieties two clusters were created, containing 64 (Kama - 61, Canadian 3) and 76 (Canadian - 67, Kama - 9) elements respectively.

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23

Table 2 Correctness percentages for the wheat varieties data set Wheat Varieties

Correctness %

Rosa Kama Canadian

96 84 96

The percentages of correctness of classification for a total of 210 samples are presented in Table 2. The proposed algorithm achieved an accuracy of about 96% for the Rosa wheat variety, 84% for the Kama wheat variety, and 96% for the Canadian wheat variety. The comparable percentages of correctness of classification has been obtained when the k-means algorithm with arbitrary taken cluster number of 3 was used. It is worth stressing however, that this algorithm availed of the a priori assumed correct number of clusters, which in many applications may not be known, or even such a “correct” – from a theoretical point of view – number might not exist at all. The CGCA instead does not require strict assumptions regarding the desired number of cluster, which allows the number obtained to be better suited to a real data structure. Moreover, in its basic form, values of parameters may be calculated automatically. However, there exists the possibility of their optional change. A feature specific to it is the possibility to influence the proportion between the number of clusters in areas where data elements are dense as opposed to their sparse regions. In addition, by the detection of one-element clusters the algorithm allows the identification of outliers, which enables their elimination or designation to more numerous clusters, thus increasing the homogeneity of the data set.

5 Conclusions The proposed clustering algorithm, based on kernel estimator methodology, is expected to be an effective technique for wheat variety recognition. It performs comparably with respect to the classical k-means algorithm, however it requires no a priori information about the data. The data reduced after applying the Principal Component Analysis, contained apparent clustering structures according to their classes. The amount of 193 kernels, giving almost 92% of the total, was classified properly. The wheat varieties used in the study showed differences in their main geometric parameters. The Rosa variety is better recognized, whilst Kama variety and Canadian variety are less successfully differentiated. Further research is needed on grain geometric parameters and their ability to identify wheat kernels.

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References 1. Charytanowicz, M., Kulczycki, P.: Nonparametric Regression for Analyzing Correlation between Medical Parameters. In: Pietka, E., Kawa, J. (eds.) Advances in Soft Computing - Information Technologies in Biomedicine. Springer, Heidelberg (2008) 2. Fukunaga, K., Hostetler, L.D.: The estimation of the gradient of a density function, with applications in Pattern Recognition. IEEE Transactions on Information Theory 21, 32–40 (1975) 3. Kowalski, P., Łukasik, S., Charytanowicz, M., Kulczycki, P.: Data-Driven Fuzzy Modeling and Control with Kernel Density Based Clustering Technique. Polish Journal of Environmental Studies 17, 83–87 (2008) 4. Kulczycki, P.: Kernel Estimators for Systems Analysis. WNT, Warsaw (2005) (in Polish) 5. Kulczycki, P.: Kernel Estimators for Systems Research. In: Kulczycki, P., Hryniewicz, O., Kacprzyk, J. (eds.) Information Technologies in Systems Research. WNT, Warsaw (2007) (in Polish) 6. Kulczycki, P.: Kernel estimators in industrial applications. In: Prasad, B. (ed.) Soft Computing Applications in Industry. Springer, Berlin (2008) 7. Kulczycki, P., Charytanowicz, M.: Bayes Sharpening of Imprecise Information. International Journal of Applied Mathematics and Computer Science 15, 393–404 (2005) 8. Kulczycki, P., Charytanowicz, M.: A Complete Gradient Clustering Algorithm Formed with Kernel Estimators. International Journal of Applied Mathematics and Computer Science 20 (2010) (in press) 9. Mirkin, B.: Clustering for Data Mining: A Data Recovery Approach. Chapman and Hall/CRC, London (2005) 10. Niewczas, J., Wo´zniak, W.: Application of “GRAINS” program for characterisation of X-ray images of wheat grains at different moisture content. In: Xth Seminar, Properties of Water in Foods, Department of Food Engineering. Warsaw Agricultural University (1999) 11. Niewczas, J., Wo´zniak, W., Guc, A.: Attempt to application of image processing to evaluation of changes in internal structure of wheat grain. International Agrophysics 9, 343– 347 (1995) 12. Rencher, M.: Methods of Multivariate Analysis. Wiley, New York (2004) 13. Silverman, B.W.: Density Estimation for Statistics and Data Analysis. Chapman and Hall, London (1986) 14. Shouche, S.P., Rastogi, R., Bhagwat, S.G., Sainis, J.K.: Shape analysis of grain of Indian wheat varieties. Computers and Electronics in Agriculture 33, 55–76 (2001) 15. Strumiłło, A., Niewczas, J., Szczypi´nski, P., Makowski, P., Wo´zniak, W.: Computer system for analysis of X-ray images of wheat grains. International Agrophysics 13, 133–140 (1999) 16. Utku, H., Koksel, H., Kayhan, S.: Classification of wheat grains by digital image analysis using statistical filters. Euphytica 100, 171–178 (1998)

Dynamics of the Clusterization Process in an Adaptative Method of Image Segmentation Aleksander Lamz˙ a and Zygmunt Wróbel

Abstract. In this paper a new method of automatic image segmentation is presented. In proposed approach a region merging method is applied, where pixels or pixel groups are merged to bigger areas. In the proposed method of the region merging seed settings, segmentation parameter definition, and number of outcoming areas determining can be ommited. Homogeneous clusters (consisting of continuous groups of pixels) are the part of the growth process. The clusters are merged when the homogeneousness condition is fulfilled. The threshold value changes during segmentation process, appropriate to the changeable conditions.

1 Introduction Image segmentation is a long standing problem in computer vision. The image segmentation process can be considered as method where specific parameter areas of a given image are distinguished [1, 2, 4, 8, 10]. A region merging method is frequently used and still modified by many researchers [2, 5, 6, 7, 8]. In the merging process some image pixels are grouped to larger areas. In the first stage of such process, so called initial pixels (seeds) are determined. After that step, the image is divided into areas which are equal to the number of initial pixels. This solution allows to decide, how many areas should be determined in the given image , and which pixels are the most typical in a given image area [1, 3]. In this paper the new automatic, adaptive method of the growth areas generating was described. Taking into account proposed algorithms, many parameter determining can be ignored, for example necessity of setting the number of outcome areas, defining the seeds and segmentation Aleksander Lam˙za · Zygmunt Wróbel Department of Biomedical Computer Systems, Institute of Computer Science, Faculty of Computer and Materials Science, University of Silesia in Katowice, ul. Bedzinska 39, 41–200 Sosnowiec e-mail: [email protected], [email protected] E. Pi˛etka and J. Kawa (Eds.): Information Technologies in Biomedicine, AISC 69, pp. 25–32. c Springer-Verlag Berlin Heidelberg 2010 springerlink.com 

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parameters. Proposed algorithm allows to decrease of the homogeneous clusters during neighbours merging procedure. Algorithm is automatically stopped, when merging procedure can not be further applied.

2 Definitions and Fundamentals In the first sequence generating, clusters merging and conception of a homogeneous cluster should be explained and defined. A homogeneous cluster is a continuous group of pixels, which fulfill the similarity condition. A group of pixels building a homogeneous cluster is labeled as Hm , where: m – the number of the following cluster. Each cluster is a set of pixels Hm = {μ1 , μ2 , ..., μi }, where μi – the gray level of a given pixel in the cluster m, i – the number of pixels in that cluster. According to that notation, we shall denote the gray level of a pixel i in a cluster m by μi (Hm ). As it was above mentioned, pixels form the cluster, and clusters should be continuous. In other words it means that each element of the cluster should have at least one neighbour of the same cluster. These are the conditions for clusters: / where m is the cluster number, M – the • No cluster can be an empty set: Hm = 0, number of clusters.  • The sum of all clusters must cover the whole image: M m=1 Hm = X, where m is the area number, M – the number of clusters, X – the set of all elements (pixels) of an image. • The clusters can not have common elements: Hm ∩ Hn = 0, / where m and n are area numbers, M – the number of areas.

3 Segmentation Algorithm There are two phases in a proposed segmentation algorithm: initial processing – generating the initial set of clusters and merging of the clusters – checking the homogeneousness condition and merging the clusters, which fulfilled that condition. In the first phase, the initial number of homogeneous clusters is generated automatically. It’s usually much bigger than expected, because some homogeneous clusters have the same parameters in different parts of a given image. In the second step the adaptive growth of the individual clusters is performed, what results from merging of the clusters that fulfil the homogeneousness condition. The number of clusters decreases when appropriate areas successive merge with their neighbours. The algorithm stops when remained clusters can not be merged.

Dynamics of the Clusterization Process in an Image Segmentation

27

3.1 Generating the Initial Set of Clusters In the first step the initial set of clusters must be determined. For this reason, in the analysed image continuous areas of pixels with similar gray levels are searched. The image is successively scanned row by row, starting at the pixel (0, 0). The algorithm for clusters building is based on recurrence. Such algorithm checking of the pixels’ neighbours and merging them to the appropriate clusters.

3.2 Merging the Clusters The main part of the proposed algorithm is the adaptive merging of the clusters that fulfil the homogeneousness condition. As the merging minimal number of the clusters for the given image is produced. The algorithm has iterative form. Each iteration consists of the following steps: • random choosing of the cluster Hm from the clusters set H, • checking the similarity condition between the cluster Hm and all its neighbours Hn , • if clusters Hm and Hn fulfil the homogeneousness condition, all elements of the neighbouring cluster are merged with the cluster Hm . In the first step the algorithm randomly chooses the cluster, which will be later checked for similarity condition. Each element of a cluster stores information about its neighbourhood. If the cluster Hm was randomly indicated, the neighborhood table for that cluster is created. To check the homogeneousness condition for every cluster Hn neighboring the Hm , the variance of the sum of elements for both clusters is computed. Based on the gray levels variance of all merged clusters elements, the homogeneousness condition is estimated. The variance estimation of a single cluster by means of equation (1) can be calculated:

σ 2 (Hm ) =

2 1 |Hm |  μi (Hm ) − μ (Hm ) , ∑ |Hm | i=1

(1)

where: σ 2 (Hm ) – the variance of the elements in the cluster Hm , |Hm | – the number of the elements in the cluster Hm , μi (Hm ) – the gray level of the element i from the cluster Hm , μ (Hm ) – the average gray level of the elements in the cluster Hm . In the proposed algorithm the variance of the two clusters’ sum (the first cluster randomly indicated, and the second one as its neighbour) is always determined.

σ 2 (Hm , Hn ) = σ 2 (Hm ∪ Hn ) The variance is calculated from the equations (3, 4):

(2)

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A. Lam˙za and Z. Wróbel

1 σ (Hm , Hn ) = |Hm | + |Hn | 2

|Hm | 

∑

2 μi (Hm ) − μ (Hm, Hn ) +

i=1

|Hn |  2  + ∑ μ j (Hn ) − μ (Hm, Hn ) ,

(3)

j=1

1 μ (Hm , Hn ) = |Hm | + |Hn |



|Hm |

|Hn |

i=1

j=1



∑ μi (Hm) + ∑ μ j (Hn )

,

(4)

where: σ 2 (Hm , Hn ) – the variance of the sum of the elements in Hm and Hn , |Hm |, |Hn | – the number of the elements in the cluster Hm and Hn , μi (Hm ), μi (Hn ) – the gray level of the element i ( j) from the Hm (Hn ), μ (Hm , Hn ) – the average gray level of all elements in the clusters Hm and Hn . When the variance of the cluster Hm and all its neighbors Hn is calculated, the algorithm chooses a neighboring cluster for which the lowest value of the variance was estimated, according to the equation (3). Then, it checks the global condition, 2 : determining if the estimated variance is smaller than the threshold value σmax 2 σ 2 (Hm , Hn ) < σmax .

(5)

If the condition is filled, the merging process begins. All elements of the cluster Hn – μ (Hn )are transferred to the cluster Hm . Then the cluster Hn is removed from the cluster set H. If the condition isn’t filled, the clusters aren’t merged and the algorithms jumps to the first step – the random choosing of another cluster.

3.3 Adaptation of the Threshold Variance In the presented algorithm the parameter responsible for determining if the clusters 2 will merge or not is the threshold variance σmax . Up to this point it’s been treated as constant. In that case for every image, regardless of objects size and texture, the segmentation would proceed in a fixed way and the results wouldn’t be satisfactory. A possible solution would be to estimate the threshold variance based on the image content, but the main purpose was to avoid any external parameters. To automatize the process a model of the threshold variance adaptation based on the segmentation process dynamics was developed. 2 As mentioned before, the value of the variance σmax has to change during the segmentation process. In a case when, in a given iteration, a cluster can’t merge with any of its neighbors, the threshold value should be adequately increased to allow the merging. On the other hand, immediate increasing this value to the needed level would result in merging all the clusters in a one cluster covering the whole image. This can’t happen.

Dynamics of the Clusterization Process in an Image Segmentation

29

2 smoothly, Therefore, a model of variance adaptation should change the value σmax not allowing it to increase excessively. Thus – when the merging doesn’t occur (the homogeneousness condition isn’t fulfilled), the threshold variance increases according to equation (6):    i 2 2 σmax (i) = σmax (i − 1) · 1 − exp − , (6) τ1

where: i – the number of the current iteration, τ1 – the time constant of the variance increase (expressed in iterations). If the clusters merge in the current iteration, the value of threshold variance decreases until the next unsuccessful merging occurs.    i − i 2 2 σmax (i) = σmax (i ) · 1 − exp − , (7) τ2 where: i – the number of the current iteration, i – the iteration, for which the last successful merging occurred, τ2 – the time constant of the variance decrease (expressed in iterations). 2 is calculated in every step of the algorithm. The The value of the variance σmax time constants τ1 (increase) and τ2 (decrease) have their values determined exper2 oscillates during the clusters’ merging. At the end of imentally. The variance σmax the segmentation process a rapid fluctuation is visible. This sudden increase of the threshold value results in merging the clusters which shouldn’t be merged. Therefore, the large area of an image is „flooded” by a single cluster. This increase was triggered by small number of clusters and a high value of variance. The unsuccessful mergings occur often, resulting in a constant increase of the threshold variance value. To avoid such situations, a parameter correcting the time constant of the variance increase (τ1 ) was introduced. During the segmentation process the number of clusters decreases successively. Along with that decrease, the time constant τ1 should increase to induce a slower rate of the threshold variance growth.

τ1 = τ0 · M0 ·

1 Mi

(8)

where: τ1 – the time constant of the variance increase, τ0 – a parameter determined experimentally, Mi – the number of the areas in the iteration i, M0 – the initial number of the areas. After introducing the correcting parameter much better results were achieved.

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3.4 Dynamics of the Merging Process Regardless of the input image characteristics, three phases can be distinguished in the course of the variance during successive iterations. Figures 1 – 3 ilustrates this fact. Three values of the variance are marked on the graphs: σ p2 – the variance for 2 – the the merged areas, σn2 – the variance for the unsuccessful merging and σmax threshold variance. The phase I – merging (Fig. 1) is characterized by a considerable frequency of changes in the merged clusters variance σ p2 with rare fluctuations of the unmerged clusters variance σn2 . It should be mentioned, that when the growth of the vari2 equals the variance of unmerged clusters after a few ance occurs, the value of σmax iterations.

Fig. 1 The values of variance in successive iterations for phase I (merging)

In the phase II – stabilization (Fig. 2) – clusters merge sporadically. The variance σn2 fluctuations occur much more often, yet they are rather homogeneous. The value 2 doesn’t reach the maximum because of the increase of the time of the variance σmax constant τ1 .

Fig. 2 The values of variance in successive iterations for phase II (stabilization)

The phase III – separation (Fig. 3) – is characterized by a visible distinction 2 . The value of the variance σ 2 is at its lowest level between the variances σn2 and σmax p and at some point it disappears, which means the process of the clusters merging is done. By the end of the second phase, the results of the segmentation are usually satisfactory. The number of clusters varies from ten to several dozen (depending on the

Dynamics of the Clusterization Process in an Image Segmentation

31

Fig. 3 The values of variance in successive iterations for phase III (separation)

(a)

(b)

(c) Fig. 4 The original image (left) and the image by the end of segmentation (right)

image complexity). The size of the merged clusters was also analysed. The Fig. 4a shows the size of merged clusters in successive iterations, and their average value. The factor k expresses the proportion between the smaller cluster and the bigger one: k=

min (|Hn | , |Hm |) max (|Hn | , |Hm |)

(9)

As we can see, the average value of k is more or less constant and oscillates around 0.4. The merging of big clusters is inadvisable, because in such cases inaccuracies in defining segments may occur. It does not happen in the first and the second phase, because the threshold variance value is then relatively low. Yet, in the third phase the merging of big clusters may at some point happen, despite of the growth of the variance increase time constant. Therefore, a modification of the clusters

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choosing algorithm in the third stage was proposed. The clusters are no more chosen by chance: only the biggest ones are checked for their possibility to merge with the smaller, neighbouring ones. This stopped big clusters from merging and precipitated the end of the segmentation process.

4 Conclusions Below some examples of segmentation for different classes of images are shown. These include real images – obtained from a microscope, computer tomography and magnetic resonance (Fig. 4). An important problem when analyzing real images is the detail level of segmentation. In the proposed algorithm segmentation details level depends on the size of the image. The presented segmentation method was tested by means of various classes of images and obtained results were very satisfactory. The details level of the image segmentation depends on the image size, hence, global segmentation can be completed with a detailed one, proceeded on chosen, earlier isolated parts of an image. In the future the proposed algorithm for colour images using HSL will be adapted.

References 1. Cour, T., Benezit, F., Shi, J.: Spectral segmentation with multiscale graph decomposition. Computer Vision and Pattern Recognition 2, 1124–1131 (2005) 2. Dhawan, A.: Medical Image Analysis. Wiley-IEEE Press (2003) 3. Gonzalez, R.C., Woods, R.E.: Digital Image Processing. Prentice Hall, New Jersey (2002) 4. Hoover, A., Jean-Baptiste, G., Jiang, X.: An Experimental Comparison of Range Image Segmentation Algorithms. IEEE Trans. Pat. Anal. and Mach. Intell. 18(7), 673–689 (1996) 5. Lamecker, H., Lange, T., Seebß, M.: Automatic Segmentation of the Liver for Preoperative Planning of Resections. In: Proceedings MMVR. Studies in Health Technologies and Informatics, vol. 94, pp. 171–174 (2003) 6. Lamza, A., Trela, M., Bialy, S., Wrobel, Z.: Agent-based method of automatic image segmentation with dynamic threshold. IEEE Signal Processing, 71–74 (2004) 7. Pantofaru, C., Hebert, M.: A Comparison of Image Segmentation Algorithms. Technical Report CMU-RI-TR-05-40, Robotics Institute, Carnegie Mellon University (2005) 8. Porikli, F.: Automatic Image Segmentation by Wave Propagation. In: SPIE Conference on Image Processing: Algorithms and Systems III, vol. 5298, pp. 536–543 (2004) 9. Soille, P.: Morphological Image Analysis: Principles and Applications. Springer, Heidelberg (2004) 10. Veenman, C.J., Reinders, M.J.T., Backer, E.: A Cellular Coevolutionary Algorithm for Image Segmentation. IEEE Transactions on Image Processing 12(3), 304–316 (2003) 11. Wang, H., Suter, D.: A Model-Based Range Image Segmentation Algorithm Using a Novel Robust Estimator. In: 3rd International Workshop on Statistical and Computational Theories of Vision, Nice, France (2003) 12. Wrobel, Z., Koprowski, R.: Praktyka przetwarzania obrazu w programie MATLAB. Wydawnictwo Exit, Warszawa (2004) 13. Zielinski, K.W., Strzelecki, M.: Komputerowa analiza obrazu biomedycznego. Wstep do morfometrii i patologii ilosciowej. Wydawnictwo Naukowe PWN, Warszawa – Lodz (2002)

Application of Adaptive Weighed Averaging to Digital Filtering of 2D Images Alina Momot

Abstract. In many biomedical fields there is a need of digital image analysis. The images often contain some disturbances in addition to the useful data. These disturbances should be reduces (or even eliminated, if it is possible) in order to improve the quality of the analysis. One of the possible methods of noise attenuation is lowpass filtering such as arithmetic mean and its generalization, namely weighted mean filtering where the weights are tuned by some adaptive algorithm. This paper presents application of Bayesian weighted averaging to digital filtering 2D images which is some modification of the existing empirical Bayesian weighted averaging method created originally for noise reduction in electrocardiographic signal. The description of the new filtering method and a few results of its application are also presented with comparison to traditional arithmetic average filtering and median filtering.

1 Introduction Image enhancement approaches fall into two broad categories: spatial domain methods and frequency domain methods. The term spatial domain refers to the aggregate of pixels composing an image. Spatial domain methods directly operate on these pixels. Spatial domain processes could be denoted by g(x, y) = T [ f (x, y)] where f (x, y) is the input image, g(x, y) is the output image and T is an operator on f , defined over some neighborhood of (x, y) [4]. The process of spatial filtering consists of moving the filter mask form point to point in an image. For linear spatial filtering the response of the filter is given by a sum of products of the filter coefficients and the corresponding image pixels in the area spanned by Alina Momot Silesian University of Technology, Institute of Computer Science, 16 Akademicka St., 44-100 Gliwice, Poland e-mail: [email protected] E. Pi˛etka and J. Kawa (Eds.): Information Technologies in Biomedicine, AISC 69, pp. 33–44. c Springer-Verlag Berlin Heidelberg 2010 springerlink.com 

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the filter mask. If all the coefficients are the same and sum up to one, this is called arithmetic mean filtering. Mean filtering is a simple, intuitive and easy to implement method of smoothing images, i.e. reducing the amount of intensity variation between one pixel and the next. It is often used to reduce noise in images. The idea of mean filtering is simply to replace each pixel value in an image with the mean (‘average’) value of its neighbors, including itself. This procedure reduces the influence of pixel values which are unrepresentative of their surroundings. Mean filtering is usually thought of as a convolution filter. Like other convolutions it is based around a kernel, which represents the shape and size of the neighborhood to be sampled when calculating the mean. Often a 3 × 3 square kernel is used, although larger kernels (e.g. 5 × 5 squares) can be used for more severe smoothing [6]. Sometimes the pixel at the center of the mask is multiplied by a higher value than any other, thus giving this pixel more importance in the calculation of the average. This is some way to reduce blurring in the smoothing process. Mask coefficients could be a discrete approximation of the 2-dimensional Gaussian distribution function [1], such Gaussian filter is an example of the weighted average filter. Like the mean filter, the median filter considers each pixel in the image in turn and looks at its nearby neighbors to decide whether or not it is representative of its surroundings. Instead of simply replacing the pixel value with the mean of neighboring pixel values, it replaces it with the median of those values. The median is calculated by first sorting all the pixel values from the surrounding neighborhood into numerical order and then replacing the pixel being considered with the middle pixel value. Median filtering could be also thought of as a convolution filter however in this case the mask coefficients are not always constant. There is only one non-zero coefficient (equal one) and which coefficient is non-zero depends on result of the sorting operation. One of the major problems with the median filter is that it is relatively expensive and complex to compute. To find the median it is necessary to sort all the values in the neighborhood into numerical order and this is relatively slow, even with fast sorting algorithms such as quicksort. The basic algorithm can, however, be enhanced somewhat for speed. A common technique is to notice that when the neighborhood window is slid across the image, many of the pixels in the window are the same from one step to the next, and the relative ordering of these with each other will obviously not have changed [2]. In the case of convolution filters where the mask coefficients are not always constant there is a need of procedure how to compute the coefficients. In 2005 Xu et al. [7] proposed adaptive fuzzy weighted average filter (AFWA) which regards the pixels in the filter window as a fuzzy set and every pixel in the filter window can be depicted by membership function, which is actually the weight of this pixel. Here author proposes a new algorithm for computing values of the mask coefficient based on the existing empirical Bayesian weighted averaging method created originally for noise reduction in electrocardiographic signal [5]. The performance of the

Application of Adaptive Weighed Averaging to Digital Filtering of 2D Images

35

new algorithm is experimentally compared with the traditional average filtering and median filtering for both synthetic and real images.

2 Weighted Averaging Methods Below there is presented the original empirical Bayesian weighted averaging method (EBWA) created for noise reduction in electrocardiographic (ECG) signal and next there is presented its modification to computing the mask coefficients for adaptive linear spatial filtering. ECG signal is characterized by quasi-cyclical, repetitive pattern that is why the needed noise attenuation may be obtained by means of averaging signals cycle-wise.

2.1 EBWA Method Let us assume that in each signal cycle fi ( j) is the sum of a deterministic (useful) signal s( j), which is the same in all cycles, and a random noise ni ( j) with zero mean and variance in the ith cycle equal to σi2 . Thus, fi ( j) = s( j) + ni ( j),

(1)

where i is the cycle index i ∈ {1, 2, . . .,M} , and j is the sample index in the single cycle j ∈ {1, 2, . . . , N} (all cycles have the same length N). The weighted average is given by M

v( j) = ∑ wi fi ( j),

(2)

i=1

where wi is a weight for ith signal cycle and v = [v(1), v(2), . . . , v(N)] is the averaged signal. The iterative weighted averaging algorithm for electrocardiographic signal can be described as follows, where ε is a preset parameter [5]: 1. Initialize v(0) . Set the iteration index k = 1. (k) 2. Calculate the hyperparameter αi for i = 1, 2, . . . , M and β (k) (k)

αi

=

∑Nj=1

β (k) =



N fi ( j) − v(k−1) ( j)

∑Nj=1

N  2 . (k−1) v ( j)

3. Update the averaged signal v(k) for kth iteration.

2 ,

(3)

(4)

36

A. Momot

(k)

v(k) ( j) =

∑M i=1 αi f i ( j) (k)

β (k) + ∑M i=1 αi

(5)

4. If ||v(k) − v(k−1) || > ε then k ← k + 1 and go to 2, else stop.

2.2 Adaptive Linear Spatial Filtering Described above algorithm could be modified for application to adaptive linear spatial filtering. In the case of 2-dimensional grayscale image the parameter N is set to one and as result it is obtained gray level of one pixel. It is worth noting that for color images the parameter N could be set to the dimension of the color space. Let us assume that r is the radius of the square mask, i.e. r = (m − 1)/2 where m is the size of mask, X and Y are dimensions of the input X × Y image f . The output image g size is (X − 2r) × (Y − 2r). For each pixel f (x, y), i.e. x ∈ {r + 1, r + 2, . . . , X − r} and y ∈ {r + 1, r + 2, . . . ,Y − r}, there is created D = (2r + 1)2 dimensional vector t = [ f (x − r, y − r), . . ., f (x + r, y + r)] based on the neighborhood of the pixel. Each pixel g(x, y) of the output image is the sum D

g(x, y) = ∑ wi ti ,

(6)

i=1

although the weights wi are not explicitly computed and the value g(x, y) is calculated by following iterative algorithm: 1. Initialize g(x, y)(0) as the arithmetic average of t. If the sample variance of t is greater than zero set the iteration index k = 1 else stop. (k) 2. Calculate the hyperparameter αi for i = 1, 2, . . . , D and β (k) (k)

αi

 −2 = ti − g(x, y)(k−1) ,

 −2 β (k) = g(x, y)(k−1) .

(7)

(8)

3. Update the average g(x, y)(k) for kth iteration. (k)

g(x, y)(k) =

∑D i=1 αi ti (k)

β (k) + ∑D i=1 αi

(9)

 2 4. If g(x, y)(k) − g(x, y)(k−1) > ε then k ← k + 1 and go to 2, else stop. Algorithm described above assumes that the values f (x, y) ∈ [0, 1]. Thus parameter (k) β (k) is always positive, although for some i the parameter αi could be undefined (k) because ti − g(x, y)(k−1) could be equal zero. For such index i the parameter αi

Application of Adaptive Weighed Averaging to Digital Filtering of 2D Images

37

(k)

should be set to a value significantly greater than other parameters αi because the pixel represented by i is equal the average g(x, y)(k−1) in kth iteration.

3 Numerical Experiments In this section there is presented performance of the described method for synthetic and real images in presence of salt-and-pepper and Gaussian noise. The noise attenuation results are compared with mean filtering and median filtering. In all experiments, using proposed averaging, the parameter ε is equal to 10−6 and for such value the number of iterations required to obtain weights for single pixel did not exceed 10 (typically equal 3 or 4). For computed output images the performance of tested methods is evaluated by the root mean-square error (RMSE) between the original image (without noise) and the output image. All experiments were run in the R environment (www.r-project.org).

3.1 Experiments with Salt-and-Pepper Noise First there are presented the noise attenuation results of the considered methods, i.e. proposed adaptive weighted averaging and traditional filtering using mean and median, for salt-and-pepper noise (appearing as white and black dots superimposed on an image). Figure 1(a) presents the synthetic grayscale image of size 256 × 256 with only 3 gray levels appearing in the image. This image was disturbed by saltand-pepper noise where the probability of the black pixel is equal 0.05 and the probability of the white pixel is also equal 0.05. The result of this procedure is presented in figure 1(b).

(a)

(b)

Fig. 1 (a) Original synthetic 3-gray level image of size 256 × 256, (b) the same image with salt-and-pepper noise

38

A. Momot

For the image from figure 1(b) there was performed filtration using all described above methods. The radius of mask was equal 2, i.e. filter mask of size 5 × 5. The output images are presented in figure 2. On the left there is the result of application square averaging filter mask, in the middle there is the result of application proposed adaptive weighted averaging method and on the right there is the result of application median filter mask.

(a)

(b)

(c)

Fig. 2 Results of noise reduction for image from figure 1(b) using:(a) mean filter, (b) adaptive weighted averaging, (c) median filter

The table 1 presents the root mean-square error between the original image, i.e. figure 1(a), and the output images 2(a), (b) or (c). It can be seen that the best result was obtained for the median filter and the worst for the mean filter. Using the proposed method results in a much better RMSE than the mean filter and slightly worse than the median filter. Table 1 Root mean-square error for noise reduction in image from figure 1(b) method

RMSE

mean filter

0.06085189

adaptive weighted averaging 0.02402858 median filter

0.02374963

Next there were performed experiments with another synthetic image with 256gray level and salt-and-pepper noise. The original and disturbed images are presented in figure 3. As in the previous noisy image, the probability of black or white pixels was equal 0.05. For the image from figure 3(b) there was also performed filtration with filter mask of size 5 × 5. The output images are presented in figure 4 and the table 2 presents the root mean-square error between the original image, i.e. figure 3(a), and the output images 4(a), (b) or (c). Next there were performed experiments with real biomedical image and saltand-pepper noise. The original and disturbed images are presented in figure 5. Like

Application of Adaptive Weighed Averaging to Digital Filtering of 2D Images

(a)

39

(b)

Fig. 3 (a) Original synthetic 256-gray level image of size 256 × 256, (b) the same image with salt-and-pepper noise

(a)

(b)

(c)

Fig. 4 Results of noise reduction for image from figure 3(b) using:(a) mean filter, (b) adaptive weighted averaging, (c) median filter Table 2 Root mean-square error for noise reduction in image from figure 3(b) method

RMSE

mean filter

0.039152

adaptive weighted averaging 0.007201034 median filter

0.0009701716

earlier, the probability of black or white pixels was equal 0.05. Square mask of size 5 × 5 filtration applied to the image from figure 5(b) gives the output images presented in figure 6 and the table 3 presents the root mean-square error between the original image, i.e. figure 3(a), and the output images 4(a), (b) or (c). In all described above experiments the best result was obtained for the median filter and the worst for the mean filter. Such results can be expected because in presence of impulse noise, such as salt-and-pepper noise, median filters are particularly

40

A. Momot

(a)

(b)

Fig. 5 (a) Original real biomedical image of size 400 × 380, (b) the same image with saltand-pepper noise

(a)

(b)

(c)

Fig. 6 Results of noise reduction for image from figure 5(b) using:(a) mean filter, (b) adaptive weighted averaging, (c) median filter Table 3 Root mean-square error for noise reduction in image from figure 5(b) method

RMSE

mean filter

0.04771754

adaptive weighted averaging 0.03733040 median filter

0.02283560

effective [4]. Using the proposed method usually results in a much better RMSE than the mean filter and slightly worse than the median filter.

3.2 Experiments with Gaussian Noise Below there are presented the noise attenuation results of the considered methods, i.e. proposed adaptive weighted averaging and traditional filtering using mean and

Application of Adaptive Weighed Averaging to Digital Filtering of 2D Images

41

median, for Gaussian noise. Figure 7 presents the 3-gray level synthetic grayscale image of size 256 × 256 and the same image disturbed by zero-mean white Gaussian noise with standard deviation equal 0.15.

(a)

(b)

Fig. 7 (a) 3-gray level synthetic image, (b) the same image with Gaussian noise

For the image from figure 7(b) there was performed filtration with filter mask of size 5 × 5. The output images are presented in figure 8 and the table 4 presents the root mean-square error between the original image, i.e. figure 7(a), and the output images 8(a), (b) or (c).

(a)

(b)

(c)

Fig. 8 Results of noise reduction for image from figure 7(b) using:(a) mean filter, (b) adaptive weighted averaging, (c) median filter

In the case of Gaussian noise it can be expected that the best result should be obtained by application the mean filter and however the results presented in table 4 shows that using the median filter has given the smallest root mean-square error, all results are similar. Possible explanation of this fact is small number of different gray levels in the original image which are concentrated in only three areas.

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A. Momot

Table 4 Root mean-square error for noise reduction in image from figure 7(b) method

RMSE

mean filter

0.04715002

adaptive weighted averaging 0.04546692 median filter

0.04463237

Next there were performed experiments with another synthetic image with 256gray level of size 256 × 256 and the same as previously described Gaussian noise. The original and disturbed images are presented in figure 9.

(a)

(b)

Fig. 9 (a) 256-gray level synthetic image, (b) the same image with Gaussian noise

For the image from figure 9(b) there was performed filtration and the output images are presented in figure 10. The table 5 presents the root mean-square error between the original image, i.e. figure 9(a), and the output images 10(a), (b) or (c).

(a)

(b)

(c)

Fig. 10 Results of noise reduction for image from figure 9(b) using:(a) mean filter, (b) adaptive weighted averaging, (c) median filter

Application of Adaptive Weighed Averaging to Digital Filtering of 2D Images

43

Table 5 Root mean-square error for noise reduction in image from figure 9(b) method

RMSE

mean filter

0.02996932

adaptive weighted averaging 0.03124959 median filter

0.03728408

In this case it can be seen that the best result was obtained for the mean filter and the worst for the median filter. Using the proposed method results in a much better RMSE than the median filter and slightly worse than the mean filter. Such results confirm the expectation for reducing of Gaussian noise. Last there were performed experiments with a real biomedical image of size 400 × 380 and the same as previously described Gaussian noise. The original and disturbed images are presented in figure 11. For the image from figure 11(b) there was performed filtration and the output images are presented in figure 12. The table 6 presents the root mean-square error between the original image, i.e. figure 11(a), and the output images 12(a), (b) or (c). In this case again, as expected, the best result was obtained for the mean filter, the worst for the median filter and using the proposed method results in a much better RMSE than the median filter and slightly worse than the mean filter.

(a)

(b)

Fig. 11 (a) Original real biomedical image, (b) the same image with Gaussian noise Table 6 Root mean-square error for noise reduction in image from figure 11(b) method

RMSE

mean filter

0.04090487

adaptive weighted averaging 0.0416553 median filter

0.04503859

44

A. Momot

(a)

(b)

(c)

Fig. 12 Results of noise reduction for image from figure 11(b) using:(a) mean filter, (b) adaptive weighted averaging, (c) median filter

4 Conclusions Results of performed experiments show that proposed adaptive weighted averaging filtering method is close to optimal for both salt-and-pepper and Gaussian noise. In reality noise is usually characterized by mixture of these two types and author expects that the new method could be useful in application to real images. The main disadvantage of the proposed method is its computational complexity significantly greater than the mean filtering and similar to the median filtering. However it is worth noting that the iterative procedures to obtain weights for each pixel in image could be performed parallel. Lately NVIDIA has developed the CUDA programming model and software environment to let programmers write scalable parallel programs using a straightforward extension of the C language [3]. Thus author intends to implement the proposed method in the CUDA environment.

References 1. Brandt, S.: Statistical and Computational Methods in Data Analysis. Springer, New York (1997) 2. Davies, E.R.: Machine Vision: Theory, Algorithms and Practicalities. Academic Press, San Diego (1990) 3. Garland, M., et al.: Parallel Computing Experiences with CUDA. IEEE Micro. 28(4), 13–27 (2008) 4. Gonzalez, R.C., Woods, R.E.: Digital Image Processing. Prentice Hall, Upper Saddle River (2002) 5. Momot, A.: Fuzzy Weighted Averaging of Biomedical Signal Using Bayesian Inference. In: Man-Machine Interactions. Advances in Intelligent and Soft Computing, vol. 59, pp. 133–140 (2009) 6. Vernon, D.: Machine Vision: Automated Visual Inspection and Robot Vision. PrenticeHall, New York (1991) 7. Xu, Q., et al.: Adaptive Fuzzy Weighted Average Filter for Synthesized Image. In: Gervasi, O., Gavrilova, M.L., Kumar, V., Laganá, A., Lee, H.P., Mun, Y., Taniar, D., Tan, C.J.K. (eds.) ICCSA 2005. LNCS, vol. 3482, pp. 292–298. Springer, Heidelberg (2005)

Photodynamic Image e-Atlas in Diagnostic and Treatment Procedures Ewa Pietka, Aleksander Sieron, Dominik Spinczyk, Przemyslaw Szabelak, Sebastian Kwiatek, and Jakub Murawski

Abstract. There is a rapidly growing interest in electronic atlases including images with medical reports and quantitative description of pathological regions of interest. The e-atlases are mostly used by students and residents for teaching and training. However, an atlas my also be employed in everyday clinical practice. An imaging system that integrates an e-atlas of photodynamic studies with computer assisted diagnostic and therapeutic procedures is presented. Image processing results are stored in the database and may also be applied in the teaching and training process. The e-atlas includes photodynamic studies with clinical reports, location of the biopsy enter, selected points of the highest autofluorescence intensity to be subjected to the therapeutic light exposure.

1 Introduction Photodynamic diagnosis and therapy is a non-invasive procedure employed in an early stage of neoplastic diseases. It improves the detection of neoplastic tissues that may not be visible in traditional procedure with white endoscopy light. Photodynamic diagnostics is based on natural phenomenon of light emission from tissues after excitation with laser light of endogenous and exogenous substances selectively absorbed in neoplastic tissues. Autofluorescence images show pathological tissues as pseudo-color in red color scale and healthy tissue as green color scale. Clinical

Ewa Pietka · Dominik Spinczyk · Przemyslaw Szabelak · Jakub Murawski Silesian University of Technology, Gliwice, Poland e-mail: [email protected], [email protected], [email protected], [email protected] Aleksander Sieron · Sebastian Kwiatek Department of Internal Diseases, Angiology and Physical Medicine, Center for Laser Diagnostics and Therapy, Bytom, Poland e-mail: [email protected], [email protected] E. Pi˛etka and J. Kawa (Eds.): Information Technologies in Biomedicine, AISC 69, pp. 45–52. c Springer-Verlag Berlin Heidelberg 2010 springerlink.com 

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experiences indicate [1, 2, 3, 4] that red color intensity is highly correlated with histological stage of neoplastic tissue. The demand of an imaging system that manages a data repository and assists the medical diagnosis and therapy has become stronger and stronger. Since human observation is influenced by internal (coming form the observer) as well as external (often independent from the observer) impacts, the system is required to increase the objectivity and speed up the decision process. An access to clinical image data with medical reports and image analysis findings is also descried for student education and training attended by residents. An imaging system requires two components which influence its effectiveness [5]. The first one is associated with an image processing methodology, the other deals with the data visualization or, in general, with a user friendly graphical interface. An overall "intelligent" workstation design becomes an important chain in modern medical diagnosis and therapy. The photodynamic imaging e-atlas developed in this study supports the patient and image data acquisition, storage and communication as well as assists the physicians in selecting the point of the highest autofluorescence intensity for the biopsy and directs the light to the area of the skin where the photosensitize drug has been admitted. The system contains three modules, namely image acquisition, image archive and presentation, computer aided diagnosis and therapy. The following sections present the structure and integration of the these modules.

2 Acquisition Module The acquisition module has been developed in order integrate the archive and presentation module with the existing acquisition station (Fig. 1). The local acquisition station registers the endoscopic images and stores them in a file system of a local workstation. The system is lacking the access policy, hierarchy, concurrent access, and data structure. In this study a data structure has been built. The hierarchy reflects the dataflow. Patient data is introduced and assigned to the patient visit. Then, the interface scans the local directory (Fig. 2), indicates new data and (if required) transfers it to the patient record in the database. Thus, the visit record is updated by adding a single image or an image series. The management of the patient data, image data and medical reports is supported by the image archive and presentation module.

3 Image Archive and Presentation Module The image archive and presentation module is based on a three-layer structure. It contains a data layer, an application layer, and a presentation layer.

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Fig. 1 System architecture

At the first layer a database management system (DBMS) is selected. It is responsible for the data archive and distribution. There are certain features that the database engine has to provide. They do not differ significantly from a general database system, yet some of them are of particular importance. Authorized access to the data, shared among various users and processes, has to be granted remotely. Security constrains define rules to be checked whenever an access is attempted to sensitive data. Different constrains need to be established for each type of access (retrieve, insert, delete, etc.) to each piece of information in the database. Inconsistency need to be avoided particularly when a standard set of data is built. All data updates have to be propagated. Integrity (i.e. ensuring that the data in the database is correct) should be maintained. Centralized control of the database can help in avoiding such problems by permitting the data administrator to define (and the DBMS to implement) integrity constraints [6]. Discussing the database structure one has to keep in mind, that a medical database contains various types of information. Since the data layer stores the images and the corresponding data, a patient record contains alphanumerical data (patient data, medical reports), images (a single image or an image series), regions of interest selected from a diagnostic image, extracted features, user data etc. The data repository can be entered for clinical as well as education purpose (Fig. 3). The aim of the clinical unit is (1) to update the medical record and (2) present the data during medical procedures. First, the database is searched by the patient name or patient ID. Medical fields including reports, the histopathological

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Fig. 2 Image acqusition management window

record, image processing findings are updated. Image processing tools, required for the quantitative image description are incorporated into the computer aided diagnosis and therapy module and described in Sec. 4. Patient data already stored in the data repository is then available for clinical performance. A monitoring of the patient therapy by comparing follow-ups is also granted. For education, a Teaching and Training Unit has been developed. The database is searched by diseases. All studies collected in the database are accessible from the Teaching and Training Unit level. Two access modes are available. One refers to the teaching activity, the other one (the training mode) permits also a user to train the preparation of complete medical report. For teaching purpose the entire anonymous patient record is displayed. Thus, image data with the corresponding medical record describing the case is presented to the user. A student can enter all available cases of a particular disease. In the Training Unit only the image data is shown and the user may try to report it. Thus, the user selects a particular disease. Then, a randomly selected image data of one patient is displayed without a report. The student/resident reports the case and then compares it with the medical record of this patient that has been prepared by an expert. The system allows also the computerized image analysis to be trained. A delineation of the region of interest has been implemented as an interactive process of locating elements using vector graphics elements in an application working on the client side (in a web browser). Circles, polygons consisting of segments or Bezier curves may be applied to outline a region (Fig. 4). A region delineated by a student working in the training mode is then compared with an region selected by an expert.

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Fig. 3 Flow chart of the e-atlas integrated with CAD and CAT procedures

The ROI selection and analysis procedures are included in the computer assisted diagnosis and treatment module (as described in the following section). The content of database is available to the authorized user through the graphical user interface (GUI) referred to as the presentation layer. The GUI offers an access to the data through navigation panels in a web browser window. A main bar on the top of the GUI window contains links to the Teaching and Training Units, help and the data acquisition module. In order to provide an access at various levels, four types of a user account have been created: read and write all, read and write new examination, read only, read only anonymous data. The read and write as well as read only modes are assigned to clinicians, whereas the later is given to students and residences for teaching and training.

4 Computer Aided Diagnosis and Therapy The e-atlas incorporates image analysis procedures able to assist the diagnosis and treatment procedure. The analysis includes the quantification analysis, region of interest segmentation, location of the biopsy enter, location of the target tissue subjected to the therapeutic light exposure. The analysis starts with a background removal that features a high red to green colour components ratio that serves as a feature in further image processing. The analysis is performed on a grayscale representation of the image, which allows the threshold used for the background removal to be adjusted. The gray scale representation image is generated with a commonly used formula

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Fig. 4 Selecting regions of interest

Y = 0.3 · R + 0.59 · G + 0.11 · B

(1)

where: R, G, B are red, green and blue colour components of the saturated image. The threshold value is selected at the very periphery of the image close to the image edge. The segmentation result is presented on the separate tab in the application window. The background pixels are removed form the colour image as well. The next step of the image analysis is the quantification of the colour values. A Numerical Colour Value (NCV) is defined as the ratio of a red colour components to green colour components in each pixel [1]. A histogram of the NCV matrix is found and employed for the ROI selection (Fig. 5). Displayed to the clinician it permits the threshold value to be adjusted. Since the threshold value is case-dependant (depends on the type of tissue and type of disease), it is selected by the clinician. Then, a region of interest is selected. In a separate image a set of points corresponding to the selected regions is superimposed over the original image. Within the ROI the greatest value of the NCV is found and marked in the image. It shows the point to be confirmed by the histological procedure. When using the programme a user can observe all four stages on the tab control placed in the main window of the application. The original photodynamic image with the NCV value and the pixel position can be tracked when moving the camera.

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Fig. 5 Sample NCV mask

The procedure permits also follow-ups to be compared. The entire analysis is performed after a treatment therapy has been applied to the patient. The images are subjected to the thresholding procedure, following by the NCV analysis. During the therapy, the light activates oxygen molecules that destroy certain types of cancer cells. The light source needs to be directly applied to the target tissue for a specific period of time [7]. A navigation system for the surface skin therapy has been built. It navigates the light source in order to direct the light to the area of the skin where the photosensitize drug has been admitted. The system contains a smart robotic arm used to fix the light source and direct the light to the target. The position of the arm is controlled by a navigation system which sets the required angle and distance above the tumor tissue and changes it during the procedure. The navigation is also supported by the image analysis. Once the red to green colour component map is also found, the region of interest is selected as described above. It shows the cancer and precancer area to be subjected to the light exposure.

5 Results The e-altas includes a set of 150 clinical cases, including images of Barrett’s esophagus, esophageal cancer, gastric ulcers, gastric cancer, colitis ulcerosa, many types of polyps in colon, solitary rectal ulcers, colonic cancer, rectal cancer and also skin lesions like Morbus Bowen, Basal Cell Carcinoma, Squamous Cell Carcinoma, and actinic keratosis, oral lesions like oral leukoplakia and oral cancer, images captured during AFL bronchoscopy with many types of epithelial lesions to be displayed by GUI. A user can interactively indicate abnormalities. The NCV (red to green colour components ratio of pixel) analysis has been implemented. The comparison of

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normal and pathological cases is also available. All studies with medical reports have been collected at the Clinical Department of Internal Diseases, Angiology and Physical Medicine in Bytom. Before being archived in the database, all cases have been histopathologically confirmed.

6 Summary Autofluorescence and photodynamic diagnostics allows the detection of small focal neoplastic tissues even not visible in traditional white light endoscopy. An imaging system that acquires the image data from a local workstation and archives it in a data repository has been built. Then, using the computer aided diagnosis module, processing functions are applied and assist physicians during the region of interest analysis. The data repository is used for both clinical and educational purpose. An access to photodynamic studies increases the knowledge in the area of photodynamic diagnosis and treatment and shows its importance in the early stage of neoplastic diseases. Acknowledgements. This work is founded by the MNiSW grant No. N R13 0049 04/2008.

References 1. Sieron, A., Gibinski, P., Pustelny, T., Kwiatek, S., Opilski, Z., Krawczyk-Krupka, A., Woznica, W., Maciak, E., Kubica, W., Urbanczyk, U., Latos, W.: Optical biopsy using spectral camera in BCC nad oral leukoplakia. Photodiagnosis and Photodynamic Therapy 5, 271–275 (2008) 2. Svanberg, K., Klintenberg, C., Nilsson, A., Wang, I., Andersson-Engels, S., Svanberg, S.: Laser-based spectroscopic methods in tissue characterization. Ann. NY Acad. Sci. 838, 123–129 (1998) 3. Won, Y., Hong, S.H., Yu, H.Y., Kwon, Y.H., Yun, S.J., Lee, S.C., Lee, J.B.: Photodetection of basal cell carcinoma using methyl 5-aminolaevulinate-induced protoporphyrin IX based on fluorescence image analysis. Clin. Exp. Dermatol. 32(4), 423–429 (2007) 4. Sieron, A., Kwiatek, S.: Twenty years of experience with PDD and PDT in Poland - Review. Photodiagnosis and Photodynamic Therapy 6, 73–78 (2009) 5. Pietka, E., Gertych, A., Witko, K.: Informatics Infrastructure of CAD system. Comp. Med. Img. Graph. 29, 157–169 (2005) 6. Date, C.J.: An Introduction to Database Systems. Addison-Wesley, Reading (2000) 7. Panjehpour, M., Julius, C.E., Phan, M.N., Vo-Dinh, T., Overholt, S.: Laser induced fluorescence spectroscopy for in vivo diagnosis of nonmelanoma skin cancers. Lasers Surg. Med. 31(5), 367–373 (2002)

Multiseries MR Data in Brain Tumours Segmentation Jacek Kawa, Paweł Szwarc, Barbara Bobek-Billewicz, and Ewa Pi˛etka

Abstract. The paper deals with the segmentation of brain tumours in magnetic resonance (MR) images. The segmentation method developed is based on the analysis of two MR series, and namely contrast enhanced T1W images and perfusion maps. The contrast enhanced T1W images are segmented with the use of the Kernelised Weighted C-Means (KWCM) method, yielding a binary mask of the suspected tumour. Next, the mask is superimposed over the perfusion maps. The perfusion intensities of corresponding areas in both brain hemispheres are compared. The results obtained for three subjects with glioblastoma multiforme (GBM) and anaplastic astrocytoma (AA) are discussed.

1 Introduction Brain tumours remain one of the most difficult tumours to be treated as they often affect areas where the treatment of choice, namely the total tumour resection, is virtually impossible. Correct decisions concerning surgery, radiotherapy and Jacek Kawa · Paweł Szwarc · Ewa Pi˛etka Silesian University of Technology, Gliwice, Poland e-mail: [email protected], [email protected], [email protected] Barbara Bobek-Billewicz Radiodiagnostics Department of the Maria Skłodowska-Curie Memorial Cancer Centre and Institute of Oncology, Gliwice Branch, Gliwice, Poland e-mail: [email protected]

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chemotherapy planning strictly depend on the accurateness of tumour segmentation performed by a radiologist. This work done manually by a radiologist is a tedious and time-consuming task. The aim of this research is to create an automatic algorithm that may be a most valuable tool for radiologists, assisting them in brain tumours segmentation in MR images.

1.1 Brain Tumours Intracranial brain tumours are divided into two groups depending on the origin of cells building them: intraaxial and extraaxial tumours. Most of the intraaxial tumours consist of glial cells. These tumours called gliomas constitute some 50% of all brain tumours. Mostly, gliomas are built of astrocytal cells. These tumours comprising about 35% of all brain tumours are called astrocytomas. The glioblastoma multiforme (GBM) is an astrocytoma tumour, classified by the World Health Organisation as having the highest IVth grade of malignancy (WHO IV) and thus being one of the most aggressive tumours. The GBM’s constitute one fifth of all brain tumours [1]. The anaplastic astrocytoma is a WHO III astrocytoma, accounting for about 4% of all brain tumours [1]. These tumours are histologically very weakly delimited from healthy tissue. Necrosis, haemorrhage into the lesion and tumour angiogenesis are often to be encountered. Extended oedema is also frequently diagnosed. These characteristics make the proper delineation of high-grade astrocytomas boundaries a laborious and difficult task [1]. The relapse tendency of GBM’s, even after radical resection and intensive radioand chemotherapy treatment, results in very poor survival rates, with median survival rate with and without treatment of ca. 3 and 8 months respectively, the 3-year survival rate after GBM diagnosis being as small as 2% [1, 2]. The median survival rate for subjects with anaplastic astrocytomas ranges from 2 to 5 years [3]. Nevertheless, new treatment methods are tested and introduced, their efficiency being dependent on the correct tumour segmentation and quantification of its volume. Thus, the assistance to radiologists in the process of the GBM segmentation in MR images proves to be extremely vital.

1.2 Nature of MR Imaging Data The segmentation method developed is based on the analysis of two MR series of subjects with diagnosed GBM or anaplastic astrocytoma, namely T1W images after the injection of Gadovist contrast agent and perfusion maps obtained on the basis of Perfusion-Weighted Imaging (PWI) series by means of manufacturer’s software. The images were acquired with a 3.0T Phillips MR and a 1.5T Siemens MR. Both imaging series are transverse-type and made with the same angle positioning in coronal and sagittal planes. The use of a contrast agent allows the regions of broken brain blood barrier to be separated. The enhancement of signal intensity, resulting

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from the shortening of the T1 time and caused by the accumulation of gadolinium compounds, is best to be noticed in T1W images. The irregular, ring-shaped signal intensity enhancement, specific for GBM’s [4], is well to be seen in most of the images. PWI plays an important role in treating primary brain tumours, as it makes it possible to find the most malignant part of the tumour. It seems that the enhancement of the relative cerebral blood volume (RCBV), whose amount is represented by the image intensity level of the perfusion maps in the lesion area, is caused by tumour angiogenesis, which may indicate the grade of malignancy of the tumour [1]. The RCBV coefficient is also helpful in telling the actual tumour areas from the radionecrosis areas and postoperative granulation tissue, all of them being hyperintensive in T1W images after contrast agent administration. The midline structures are often displaced due to an expansive lesion, which makes it difficult to correctly establish the brain symmetry line in MR images. The brain symmetry itself may also often be disturbed by the tumour due to the mass effect [1].

1.3 Brain Tumour Segmentation Approaches Most of the approaches to brain tumour segmentation are studies on automatic segmentation algorithms, although semi-automatic methods are also common. However, none of them has yet succeeded in creating universal software able to facilitate the segmentation of all kinds of brain tumours. The difficulty of the problem lies mainly in the variety of shapes and locations of lesions. As far as semi-automatic brain tumours segmentation methods are concerned, the most widespread algorithms are defined respectively as seeded region growing and active contours and are dealt with for T1W contrast images [5]. In the active contours algorithm the geodesic deformable model provided by [6] and the geometric active contours method based on the theory of curve evolution were implemented [5]. Various approaches to the automatic brain tumour segmentation have been applied. One-class Support Vector Machine (SVM) was developed to separate tumour and non-tumour regions in [7]. Structural analysis-based tumour segmentation scheme was presented in [8]. The authors of [9] presented Gaussian Mixture Model (GMM) and SVM-based methods for brain segmentation.

2 Segmentation Algorithm The segmentation algorithm developed in this study consists of two phases. The segmentation of contrast enhanced T1W series is followed by the analysis of perfusion maps.

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2.1 Segmentation of Contrast Enhanced T1W Series The basic algorithm, permitting the segmentation of brain matter, cerebrospinal fluid and contrast enhanced areas in the contrast enhanced T1W series, is the Kernelised Weighted C-Means (KWCM). This method emerged directly from the standard Fuzzy C-Means (FCM) method [10, 11]. FCM is a clustering method based on the minimisation of an objective function. It divides a finite set of elements into c clusters with respect to some given criterion [11, 12]. The data clustering methods using kernel functions allow a nonlinear transposal of the data into a high-dimensional space. The KWCM method fully transposes the clustering process into that high-dimensional space [13, 14]. The Radial Basic Function (RBF) is used as kernel function for the KWCM algorithm in the software. The feature incorporated in the clustering process is the signal intensity. The FCM objective function for partitioning a dataset X = {x1 , x2 , . . . , xi , . . . , xN }

(1)

into c clusters can be defined as [11] c

J(U) =

N

β

∑ ∑ uki dki ,

(2)

k=1 i=1

β being the fuzzyfication parameter, dki the distance measure selected between the ith object and the kth cluster centre and uki the elements of U - the fuzzy partition matrix. In each t th iteration of the FCM algorithm, for each cluster k, the fuzzy cluster centre [12] β ∑N u xi (t) vk = i=1 kiβ (3) ∑Ni=1 uki is calculated using fuzzy membership values in the partition matrix U(t) . In the first iteration U(1) as well as the cluster centres are set to random values. In the next steps U(t+1) values are recomputed following the equation [12] (t+1)

uki

= ∑cj=1

1   dki d ji

1 β −1

,

(4)

where d denotes the distance metric selected. When the selected norm U(t+1) − U(t)  ≤ ε , the computations stop and the defuzzyfication makes the analysed data xi belong to the class k, if the uki fuzzy membership value is the highest of all u ji ( j = 1, . . . , c) values. The Kernelised Fuzzy C-Means (KFCM) algorithm adopts a kernel-induced distance metric, the objective function being [15]

Multiseries MR Data in Brain Tumours Segmentation

J(U, φ ) =

c

N

57

β

∑ ∑ uki φ (xi ) − φ (vk )2,

(5)

k=1 i=1

with φ denoting a nonlinear mapping function into a higher dimensional feature space. Substituting the Gaussian RBF   −x − y2 φG (x, y) = exp (6) σ2 as the kernel function and bearing in mind that φG (x, x) = 1, equation (5) can be simplified to c

J(U, φ ) = 2 ∑

N

β

∑ uki (1 − φG(xi , vk )) .

(7)

k=1 i=1

Taking the first derivative of J(U, φ ) with respect to uki and comparing it to zero yields the following equation for the fuzzy partition matrix values [15] −1

(t+1)

uki

=

(1 − φG (xi , vk )) β −1 −1

∑cj=1 (1 − φG (xi , v j )) β −1

.

(8)

The KWCM algorithm is a generalised version of the KFCM method, if the condition β ∑N u φ (xi ) (t) vk = i=1 ki β (9) ∑Ni=1 uki is imposed [16]. On the basis of the analysis of clusters and the fuzzy membership values brain matter, background, cerebrospinal fluid and suspected tumour or fat areas are segmented. The masks achieved in that way are processed with mathematical morphology operations, yielding the white and grey matter areas and thus narrowing down the region of interest. At this stage the location of lateral ventricles and eyeballs is also detected. After further automatic corrections, including the Quickhull [17] algorithm, the final suspected tumour areas mask is computed [16] (Fig. 1 and 2). In the case of high-grade astrocytomas the discontinuousness of tumour areas caused by the necrotic tissue inside the tumour is often to be encountered (Fig. 2). The necrotic tissue seems to be correctly qualified by the KWCM algorithm as nontumourous.

2.2 Perfusion Maps Analysis As already mentioned, both imaging series have the same length, angle positioning in coronal and sagittal planes and identical location of the brain in the field of view

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Fig. 1 Original contrast enhanced T1W image selected from study no. 1 of subject no. 1. (left) and the same image with the suspected tumour areas mask superimposed (right)

Fig. 2 Original contrast enhanced T1W image selected from a follow-up study of subject no. 1 (left) and the same image with the suspected tumour areas mask superimposed (right)

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of the images. The perfusion maps, originally having a 128×128 pixel resolution, are first pre-processed with the bicubic interpolation algorithm [18] to achieve the same pixel dimensions as the contrast enhanced T1W images, thus making it possible to match corresponding slices coming from two analysed series. The brain mask on the perfusion maps is found after interpolation by means of simple image thresholding and hole filling. The number of pixels common with the brain mask from the contrast enhanced T1W series, obtained during its segmentation process, is calculated. Then, the brain mask from the perfusion maps is shifted a given number of pixels in different directions. The number of pixels common with the brain mask from the contrast enhanced T1W series is calculated for each shifting. The shifting, for which the number of common pixels is the highest, is considered as the best alignment matching the two series. Next the perfusion maps are examined on the basis of their signal intensity. For each l th lesion, belonging to the final suspected tumour areas mask, the mean pixel intensity value ml is computed. The mean pixel intensity sl is also computed for the area lying symmetrically to the l th lesion in the opposite hemisphere. This requires the brain symmetry line to be located, since the head during an examination may not be centred within the field of view of an image. The symmetry line is searched in a set of candidate lines created by shifting to the left and to the right and rotating the image symmetry line. The line which has the least common pixels with the mask of brain hemispheres is considered to match best the real brain midline and is thus defined as the symmetry line. In most cases the defined symmetry line is slightly shifted and rotated in respect to the image symmetry line. If the mean pixel intensities ratio ms l < T1 , where T1 denotes the user-selected l threshold for the whole analysis of perfusion maps, the analysed lesion is classified as non-tumourous and discarded from further analysis. The user may additionally discard lesions that are less than a given number of pixels in size. For pixels belonging to the yet not discarded lesions a similar analysis is applied, i.e. pixels whose symmetry-based signal intensity ratio is less than the user-defined T2 threshold value, are rejected. This is performed in order to eliminate artefacts. The tumour areas mask is thus finally obtained (Fig. 3, 4, 5 and 6). In the tumour areas the number of pixels is calculated and multiplied by the unit voxel volume based on the DICOM data (slice thickness plus the interslice gap, which are 5mm and 1.5mm respectively for the imaging data acquired with the 1.5T MR and 4.0mm and 0.0mm respectively for the imaging data acquired with the 3.0T MR), yielding the final tumour volume.

3 Results The tests have been performed on MR data of three subjects with diagnosed highgrade astrocytomas, namely one subject with GBM (subject no. 1) and two subjects with anaplastic astrocytoma (subjects no. 2 and no. 3). For one subject three consecutive MR studies were available. For each of the other subjects there was one MR study available. Four studies performed on the 1.5T MR consisted of 19 slices and

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Fig. 3 Original contrast enhanced T1W image selected from study no. 1 of subject no. 1. (left) and the same image with the final tumour areas mask superimposed (right). An arrow indicates the postoperative granulation tissue area.

Fig. 4 Original perfusion map corresponding to the T1W contrast image in Fig. 1 (left) and the same map with the final tumour areas mask superimposed (right)

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Fig. 5 Original contrast enhanced T1W image selected from a follow-up study of subject no. 1 (left) and the same image with the final tumour areas mask superimposed (right). An arrow indicates the radionecrotic tissue area.

Fig. 6 Original perfusion map corresponding to the T1W contrast image in Fig. 2 (left) and the same image with the final tumour areas mask superimposed (right)

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one study performed on the 3.0T MR consisted of 36 slices, yielding the total of 112 slices analysed. The detailed results obtained at the subsequent steps of the segmentation algorithm are presented in Fig. 1-6. The selected images, shown in Fig. 1, 3 and 4, come from the study performed after partial resection of the tumour, before radiotherapy treatment. The exclusion of the postoperative granulation tissue, indicated by an arrow in Fig. 3 from the final tumour areas mask due to the analysis of the perfusion map is well to be noted. Radiotherapy resulted in a decrease in the tumour volume, although a hyperintensive area of radionecrotic tissue appears instead in the T1W contrast image (Fig. 2) coming from a follow-up study of the same subject. The analysis of the corresponding perfusion map resulted in the exclusion of the radionecrotic tissue area (arrow in Fig. 5), from the final tumour areas mask. All the obtained segmentation results were compared with manual segmentation verified by a radiologist. Three similarity measures were used, namely sensitivity S=

TP · 100%, T P + FN

(10)

P=

TN · 100% T N + FP

(11)

specificity

and the Dice Similarity Coefficient DSC =

2·TP · 100%, 2 · T P + FP + FN

(12)

where T P denotes the number of true positives, T N the number of true negatives, FP the number of false positives and FN the number of false negatives. The similarity coefficients for all the analysed studies are gathered in Tab. 1. In case of subjects no. 2 and no. 3 all the hyperintensive lesions in the contrast enhanced T1W series are radionecrotic tissue areas, so only specificity is calculated for these studies.

Table 1 Automatic Segmentation Results Subject no.

Study no.

S(%)

P(%)

DSC(%)

1 1 1 2 3

1 2 3 4 5

80.965 78.892 67.736 -

99.924 99.944 99.963 99.928 99.971

74.381 75.630 67.218 -

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4 Conclusions The brain tumours segmentation results achieved by using the segmentation algorithm described above seem to be very promising. Future work will include further improving the segmentation method and performing tests on a larger amount of imaging data of subjects with diagnosed high-grade gliomas as well as on MR images of subjects with other types of brain tumours. Acknowledgements. The MR data was made available by courtesy of the Radiodiagnostics Department of the Maria Skłodowska-Curie Memorial Cancer Centre and Institute of Oncology, Gliwice Branch.

References 1. Brant, W.E., Helms, C.A.: Fundamentals of Diagnostic Radiology, vol. I. MediPage, Warszawa (2007) (Polish translation) 2. Krex, D., Klink, B., Hartmann, C., et al.: Long-Term Survival with Glioblastoma Multiforme, http://brain.oxfordjournals.org/cgi/content/full/ 130/10/259 3. Kennedy, B., Bruce, J.N.: Astrocytoma (2009), http://emedicine.medscape.com/article/283453-overview 4. Runge, V.M.: Clinical MRI. Elsevier Urban and Partner, Wrocław (2007) (Polish translation) 5. Salman, Y.M., et al.: Validation Techniques for Quantitative Brain Tumours Measurement. In: IEEE Engineering in Medicine and Biology 27th Annual Conference, Shanghai, China (2005) 6. Kimmel, R., Caselles, V., Sapiro, G.: Geodesic Active Contours. International Journal on Computer Vision 1, 61–97 (1997) 7. Zhou, J., et al.: Extraction of Brain Tumour from MR Images Using One-Class Support Vector Machine. In: IEEE Engineering in Medicine and Biology 27th Annual Conference, Shanghai, China (2005) 8. Xuan, X., Qingmin, L.: Statistical Structure Analysis in MRI Brain Tumour Segmentation. In: Fourth International Conference on Image and Graphics, Chengdu (2007) 9. Hongmin, C.: Probabilistic Segmentation of Brain Tumours Based on Multimodality Magnetic Resonance Images. In: Fourth IEEE International Symposium on Biomedical Imaging From Nano to Macro, Washington, DC (2007) 10. Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press, New York (1981) 11. Xu, R., Wunsch, D.: Survey of Clustering Algorithms. IEEE Transactions Neural Networks 16, 645–678 (2005) 12. Mekhalfa, F., Goumeïdane, A.B., Nacereddine, N.: Unsupervised Algorithm for Radiographic Image Segmentation Based on the Gaussian Mixture Model. In: EUROCON 2007 The International Conference on Computer as a Tool, Warsaw (2007) 13. Girolami, M.: Mercer Kernel-Based Clustering in Feature Space. IEEE Transactions Neural Networks 13, 780–784 (2002) 14. Wu, Z., et al.: Fuzzy C-Means Clustering Algorithm Based on Kernel Method. In: 5th International Conference on Computational Intelligence and Multimedia Applications (ICCIMA 2003), Xi’an, China, pp. 49–54 (2003)

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15. Zhang, D., et al.: Kernel-Based Fuzzy Clustering Incorporating Spatial Constraints for Image Segmentation. In: Proceedings of the Second International Conference on Machine Learning and Cybernetics, Xi’an, China (2003) 16. Kawa, J.: Fuzzy Methods in Segmentation of Demyelination Plaques in Brain MR Images, PhD Thesis, Silesian University of Technology, Department of Automatic Control, Electronics and Computer Science, Institute of Electronics, Gliwice (2007) (in Polish) 17. Barber, C.B., et al.: The Quickhull Algorithm for Convex Hulls. ACM Transactions on Mathematical Software 22, 469–483 (1996) 18. Keys, R.G.: Cubic Convolution Interpolation for Digital Image Processing. IEEE Transactions on Acoustics, Speech and Signal Processing ASSP 29, 1153–1160 (1981)

Symmetry Plane of the Brain on Perfusion MR Images Rafał Henryk Kartaszy´nski and Paweł Mikołajczak

Abstract. In this paper we present algorithm which purpose is to estimate real symmetry plane of the brain on the MRI perfusion studies. Because perfusion slices are acquired in low resolution and larger distances, than standard MR studies, symmetry plane of the brain must be evaluated on the slice-by-slice basis. Presented algorithm therefore searches for symmetry line taking into consideration only anatomical information on each slice, ignoring adjacent slices. After presenting the method and sample results, we present results of tests.

1 Introduction Perfusion MRI study [1, 2] is based on the use of injected contrast agent that changes the magnetic susceptibility of blood and thereby the MR signal which is repeatedly measured during bolus passage. Because images must be acquired very quickly and often, quality must be reduced and distance between slices increased. As the result of one study we get about 400 - 500 images (about 10 images per 40 passes). Fig. 1 shows example set of images acquired by a single pass. As is known brain consists of two symmetrical cerebral hemispheres. Often to check for abnormalities, differences, two adjacent hemispheres on the same image are compared. To automatize this process, there is a need to find the symmetry plane of the brain. In this article we are using the term symmetry line/plane to describe a symmetry plane of the brain itself, not symmetry line of the data on image. Because image acquisition plane is not perpendicular to the brain symmetry plane, acquired slices rarely show symmetrical image (Fig. 1). Therefore only chance to find a symmetry plane is to find anatomical structures that appoint it. Rafał Henryk Kartaszy´nski · Paweł Mikołajczak Maria Curie Skłodowska University, Maria Curie-Skłodowska 1 square, 20 - 031 Lublin, Poland e-mail: [email protected], [email protected] E. Pi˛etka and J. Kawa (Eds.): Information Technologies in Biomedicine, AISC 69, pp. 65–72. c Springer-Verlag Berlin Heidelberg 2010 springerlink.com 

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Fig. 1 Example MRI perfusion study (first pass) - part 1

Because this algorithm is to be used as a part of semi-automatic methods for comparing images of both cerebral hemispheres, we do not require it to be very correct. 1-2 degree deviation is acceptable.

2 Method Due to the distance between slices, we are evaluating symmetry lines for each slice separately - we are not treating set of slices as a complete volume. Method itself can be divided into following steps: 1. Data preprocessing 2. Finding of the Characteristic Points (CP) 3. Linear regression One of the main assumption of this algorithm is that brain symmetry line is not deviated more than about 10-15 degrees from the AP axis.

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Fig. 2 Example MRI perfusion study (first pass) - part 2

3 Data Preprocessing First step of presented algorithm is to remove background noise and other tissues surrounding brain. This can be achieved by simple thresholding to the certain value. By analyzing looks of the general histogram of the MRI perfusion slice (Fig. 3) we can find two main peaks on in. First on the left, represents numerous low frequency background pixels. With increasing intensity of pixels (to the right of the diagram) this peak / number of pixels decreases reaching local minimum (I0) and increasing again to reach another local maximum (IB). In general case of MRI study segmentation at the level I0 would be sufficient, but in the case of the perfusion images and for needs of this algorithm (see another step of the algorithm) we need a deeper segmentation. Therefore we have set the threshold value at IP = I0 +

(IB − I0 ) 4

(1)

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Fig. 3 General histogram for the MRI perfusion slice

4 Finding Characteristic Points To have some starting point for estimation of symmetry line algorithm is finding notches between hemispheres in the front and the back of the brain (Fig. 4). To find them image is scanned from beginning and from end line-by-line. According to assumption of brain not being too much rotated, we are narrowing the search to the 25% middle of the image (vertical trench). In the case of an average slice having 120x120 pixels, this trench would be 30px wide. Generally we are looking for the deepest (closest to the middle of the brain) notch in the front and back tissue of the brain. If there are several notches found, on the similar deepness and the difference (in deepness) is not greater than 2% (of the whole image size) then problem is not resolved and no CP is found. The same situation is when the notch is to wide (more than 4%) - de facto there is no notch (Fig.4.).

Fig. 4 First two CP (on the right). Case when one of the CP cannot be found (on the left).

From obvious reasons finding of these points is not always possible - on some slices there are no notches detectable. Also sometimes these points can be badly found, so they cannot be the only CP used to fit symmetry line into. Therefore

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we have also incorporated method for finding other anatomical structures that can describe symmetry plane of the brain. To do this we are continuing to scan-line the trench between first two CP or places where previous step have ended. The algorithm is searching for local minima or maxima on these scan lines that have local maxima or minima, respectively, on both its sides (see Fig. 5). On this figure one can see ideal cases that do not leave place for misinterpretation. And only such cases are used later. We do not need a lot of points in later step of the algorithm - linear regression. Most important is quality and accuracy of these points. Of course in many cases good points will be found on adjacent scan lines. For each set of six points that are adjacent (occupy six neighbouring horizontal lines) middle one is selected as CP to represent all six points. Thanks to this step, only reasonable number of CP will be used in regression.

Fig. 5 Horizontal scan lines of the trench for two different slices

5 Perpendicular Regression Given a set of Characteristic Points it is possible to fit a straight line into this set by using linear regression [3, 4, 5]. When we perform a regression fit of a straight line to a set of (x, y) data points we typically minimize the sum of squares of the vertical distance between the data points and the line. However in this case we have to optimize the perpendicular distances to the line. One way of approaching this is to find the principle directions of the data points. Let’s say we have the (x, y) coordinates of n data points. To make it simple, let’s first compute the average of the x values, and the average of the y values, calling them X and Y respectively. The point (X,Y) is the centroid of the set of points. Then we can subtract X from each of the x values, and Y from each of the y values, so now we have a list of n data points whose centroid is (0, 0). To find the principle directions, imagine rotating the entire set of points about the origin through an angle q. This sends the point (x, y) to the point (x’, y’) where

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x = x ∗ cos(q) + y ∗ sin(q)

(2)

y = −x ∗ sin(q) + y ∗ cos(q)

(3)

Now, for any fixed angle q, the sum of the squares of the vertical heights of the n transformed data points is S = ∑ [y ]2 , and we want to find the angle q that minimizes this. (We can look at this as rotating the regression line so the perpendicular corresponds to the vertical). To do this, we take the derivative with respect to q and  set it equal to zero. The derivative of [y ]2 is 2y ( dy dq ), so we have dS = 2 ∑ [−x ∗ sin(q) + y ∗ cos(q)][−x ∗ cos(q) − y ∗ sin(q)] dq

(4)

We set this to zero, so we can immediately divide out the factor of 2. Then, expanding out the product and collecting terms into separate summations gives [∑ x ∗ y] ∗ sin2 (q) + [∑ (x2 − y2 )] ∗ sin(q) ∗ cos(q) − [∑ x ∗ y] ∗ cos2 (q) = 0

(5)

Dividing through by cos2 (q), we get a quadratic equation in tan(q): x ∗ y ∗ tan2 (q) + x2 − y2 ∗ tan(q) − x ∗ y = 0

(6)

where the curly braces indicate that we take the sum of the contents over all n data points (x, y). Dividing through by the sum x ∗ y gives tan2 (q) + A ∗ tan(q) − 1 = 0

(7)

−y where A = x x∗y . Solving this quadratic for tan(q) gives two solutions, which correspond to the principle directions, i.e., the directions in which the scatter is maximum and minimum. We want the minimum. Having the angle q we can find symmetry line, which is passing through the centroid of the data. 2

2

6 Results and Tests Following are the sample results, obtained by presented method. We have tested this method on ten data sets from two sources - Clinical Hospitals. In 92% cases (failed on 8 images out of 100 - 10 first pass images from 10 studies) method have managed to find more than four CP and perform regression. We must note that images, on which the method has failed were difficult cases located in the lower parts of the brain. Generally all abnormalities that must be located by the perfusion study are located in higher parts of the brain. Therefore, for tested data sets, method proved to find CP in all diagnostic meaningful cases. To evaluate quality of symmetry lines, found by the algorithm, we have compared it’s results with ones provided by the experts. We have asked three physicians

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Fig. 6 Example results of symmetry line finding for the whole set

Fig. 7 Example result for the one slice (different data set)

to mark symmetry lines on first pass images from each study. Each expert received six data sets. Studies were divided in the manner that three data sets were common for each expert. This was our control set to estimate average error between expert. Because expert skills are subjective - each one will mark symmetry line little differently - we wanted to check what difference is not significant for them. As indicators for comparing two symmetry line we have compared angles (from vertical axis in means of percents of 45 degrees) and distance between these lines [6].

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First of all we have compared results for control sets. Maximal difference in distance, between experts, was about 5% (of image width in pixels). Difference in case of the angles was about 2,5% (2% of 45 degrees = 0,9 degree). Mean difference for the distance was 4% and angle about 2%. Next we have compared expert results with that acquired by presented method. Comparison showed mean difference in distance of 5,5% and 3,5% in angle. On image this differences mean about 6-7 pixels, and 1,50. We had also asked our experts to rate results obtained with our method. In their opinion algorithm produces satisfying result (only in few cases they noted that it could done better). As mentioned on the beginning of this article, algorithm will be used as a part of other methods that will statistically compare images of both cerebral hemispheres, therefore quality of found symmetry lines, even in worst cases, is very satisfying.

7 Conclusions Algorithm presented in this article may be used for finding symmetry lines on low resolution, sparse images of MRI brain perfusion studies. Because these images are acquired in specific manner, only way to locate line between cerebral hemispheres is to analyze brain anatomy. Therefore method is trying to find characteristic anatomical places that describe middle point of the brain. Using linear regression, line is then fitted into found set of characteristic points. Of course some presumptions are made for these method. First of all deviation of symmetry line from the vertical axis cannot be greater than 10-15% (which may occur only in special cases). We also do not require found symmetry lines to be perfect, small deviation from ideal are possible. After comparing acquired results with results given by experts, we have came to the conclusion that method produces satisfying results for diagnostic meaningful cases.

References 1. Thacker, N.A.: Tutorial: Functional MRI Analysis, Tina Memo No. 2001-001 (2002) 2. Phillips, M.D.: Brain Perfusion Imaging. Seminars in Cerebrovascular Diseases and Stroke 1(4) (2001) 3. Acton, F.S.: Analysis of Straight-Line Data. Dover, New York (1966) 4. Chatterjee, S., Hadi, A., Price, B.: Simple Linear Regression. In: Regression Analysis by Example, 3rd edn., ch. 2, pp. 21–50. Wiley, New York (2000) 5. Edwards, A.L.: The Regression Line on. In: An Introduction to Linear Regression and Correlation, ch. 3, pp. 20–32. W.H. Freeman, San Francisco (1976) 6. Eberly, D.: 3D Game Engine Design, Section 2.6. Distance Methods (2001)

A Two-Step Method for Detection of Architectural Distortions in Mammograms Magdalena Jasionowska, Artur Przelaskowski, Aleksandra Rutczynska, and Anna Wroblewska

Abstract. Early detection of breast cancer is very important. It increases breast cancer treatment and reduces mortality rates by 30 - 70%. Architectural distortion (AD) is one of the commonly missed signs of breast cancer. It is estimated that 12 - 45% of missed breast cancer in mammography are ADs. Our ultimate goal is to develop a CAD module through creating of ADs detection method (ArDist method). We rely on fact that AD is a group of line structures of different orientation. The ArDist method consists of two stages: detection of ROI with potential ADs based on analysis with Gabor filters (GF method) and recognition of ADs using 2D Fourier transform in polar coordinates (DD method). The method was tested with 33 mammograms containing ADs, from the database DDSM. Experimental results are promising in comparison with the results of the model method and the efficiency of commercial CAD systems. The sensitivity of ArDist method amounts to 68% with 0.86 false positives per image.

1 Introduction Screening mammography is the most effective tool for early detection of breast cancer. There are three typical types of abnormal findings: microcalcifications, masses and architectural distortions [7]. Early detection of them increases breast cancer treatment and the survival rate. However, the sensitivity of screening mammography which is affected by many elements (e.g. image quality, the radiologist’s level of expertise) is not perfect. In screening mammography only 3% of detected by Magdalena Jasionowska · Artur Przelaskowski · Aleksandra Rutczynska Institute of Radioelectronics, Warsaw University of Technology, Nowowiejska 15/19, Warsaw, Poland e-mail: [email protected], [email protected], [email protected] Anna Wroblewska Wyzsza Szkola Przedsiebiorczosci i Nauk Spolecznych, Armii Krajowej 13, Otwock, Poland E. Pi˛etka and J. Kawa (Eds.): Information Technologies in Biomedicine, AISC 69, pp. 73–84. c Springer-Verlag Berlin Heidelberg 2010 springerlink.com 

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radiologists lesion are architectural distortions, whereas 61% of detected findings are mass, microcalcifications - 90% [4]. Therefore, we develop one of CAD modules in order to aid radiologists in ADs detection.

1.1 Architectural Distortion Architectural distortion (AD) is a subtle sign of abnormality in mammography (Fig.1a). This finding is a breast lesion in which the normal structure of the breast parenchyma is distorted as if being pulled into a central point, without a visible central density [2]. AD is a single sign or an early sign of breast cancer [7]. During

Fig. 1 (a) ROI containing architectural distortion with spiculations radiating and (b) ROI with radial scar - a benign lesion of the breast [6, 7]

description of mammograms radiologists can make mistakes - the views of scarring from previous surgery, radial scar1 (Fig.1b) and crossing breast structures can be diagnosed as architectural distortions. Architectural distortions have indefinite characteristic features, e.g. number of spicules, width and length of spicules, density. It makes difficulties in detection process.

2 Materials Several automated methods for ADs detection have been reported. All of them rely on fact that AD is a group of line structures of different orientation. The particulars about detecting process are described in [8, 9, 15, 17]. The six following stages can be distinguished: 1

Radial scar - a complex sclerosing lesion; it has a black star appearance with long, thin spicules radiating from a radiolucent central area.

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1. breast segmentation - mammogram segmentation into breast region and background, usually using region growing methods; 2. preprocessing of mammogram - preliminary filtering in order to sharpen the spicules of ADs and reduce the noise; 3. enhancement of spicules - extracting of texture orientation (line structures of different orientation): • filtering in the Radon domain; basic idea is to design matched filters for the ADs features [17]; • extraction of the surface direction by the sign of the mean curvature and calculation of the concentration index (ADs correspond to the high concentration regions) [9]; • filtering with a bank of Gabor filters of different texture orientation angles [1, 14, 15]; 4. selection of ROI containing potential ADs - analysis of extracted texture orientation: • phase portrait modelling - the oriented texture is analyzed to produce three maps, whereas only one of them (a node map) is further analyzed to detect the sites of ADs [1, 14, 15]; 5. estimation of characteristic features for ADs in order to reduce the false positives: • the fractal dimension (e.g. using Hausdorff dimension or by 2D Fourier power spectrum) [8, 15]; • the following features: the size of the suspected region, the mean pixel value of the suspected region, the mean concentration index of the suspected region, the isotropic index, the contrast between the suspected region and surrounding region, two features of power spectra which are obtained from 2D Fourier transform [9]; • the Haralick’s texture measures (using the joint occurrence or co-occurrence of gray levels, known as the gray-level co-occurrence matrix) [15, 19]; 6. features classification: • using support vector machine (SVM); the SVM bases on maximization of the separating margin between the two classes: normal breast tissue and ADs [8, 10]; • using radial basis function neutral networks (RBF) [8]. The efficiencies of quoted solutions are unsatisfactorily. There is either the low sensitivity or the high number of false positives per image (FPI). Ichikawa et al. [9] received the sensitivity for detection of ADs - only 56% at FPI = 0.96. The sensitivity of ADs detection method created by Sampat et al. [17] was 80% at the unacceptable number of FPI = 14. The results of Guo et al. [8] showed that the best classification of ADs is SVM (72% correct answers). The sensitivity of 84% at a high false-positive rate of 7.4 per image was received by Rangayyan et al. [14].

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Generally, the sensitivity of interpreting radiologists and CAD systems for ADs detection is low in comparison with the other findings. The commercial CAD systems [5, 13] correctly marked 90% cases of masses and microcalcifications (it is average sensitivity of masses and microcalcifications), whereas the sensitivity of ADs detection has been reported to be only ca. 40% [16]. The R2 Image Checker system [13] successfully identified 49% cases containing ADs with 0.7 false positives per image. The CADx Second Look system [5] successfully detected 33% cases of ADs with 1.27 false positives per image [16]. Additionally, only 48 - 60% of ADs that are biopsied are found to be cancer [11, 16].

3 ArDist Method In image processing, ADs are modeled as the group of line structures of different orientation. Therefore, orientation transformations (that enhance texture orientation of image) are used in order to detect the ADs. We propose ArDist method (Fig.2) which consists of two steps: detection of ROIs with potential ADs, based on Gabor filtering (GF method) and ADs recognition in selected ROIs, using 2D Fourier transform in polar coordinates (DD method).

Fig. 2 Schema of ArDist method. The first stage - detection of ROIs with potential ADs, using Gabor filtering (GF method) and the second stage - ADs recognition in selected ROIs (DD method).

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3.1 GF Method We propose GF method based on analysis of ADs spicules (line structures of different orientation) using Gabor filters with selected impulse response. GF method consists of four steps: i) preprocessing, ii) Gabor filtering, iii) Gabor maps histogram analysis and iv) “probability map”analysis (Fig.2). It is necessary to reduce the noise and the influence of the low-frequency components of the mammogram in estimating the texture orientation. Therefore, the mammogram is low-pass and then highpass filtered. Next, we filter the mammogram with the bank of 180 Gabor filters of different orientation. The Gabor filter is a sinusoidally modulated Gaussian functions, defined as follows: 1 x y gk (x, y) = exp([− [(  )2 + (  )2 ]]) ∗ cos(2π f x ) 2 Sx Sy

(1)

where x = x cos θk + y sin θk , y = y cos θk − x sin θk , the angle of texture orientation θk ∈ [−π /2, π /2], the frequency of sinusoidal function f = 0.075, parameters that determine width of Gabor filter and elongation in the y direction: Sx = 4, Sy = 4 (Fig.3). All parameters were chosen experimentally.

Fig. 3 Gabor filter mask of size 9x9 with applied parameters: Sx = 4, Sy = 4, f = 0.075, θk = π /2

The texture orientation at a pixel is estimated as the highest magnitude of amplitude at the pixel among 180 values (for 180 corresponding filter responses). As the result of Gabor filtering we receive two Gabor maps. The map with the maximum values of amplitude M(x, y) (Fig.4b) is estimated as the highest magnitude of amplitude among 180 values of different orientation (for 180 corresponding filter responses). The second map Q(x, y) contains the dominant texture orientation angles (Fig.4c), i.e. angles for which the magnitude of amplitudes is maximum). In order to select ROIs with potential ADs, histogram analysis of Gabor maps is employed by blocks K × K pixels and as the result a “probability map”is created. ADs spicules are characterized by high magnitude of amplitudes. Therefore,

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(a)

(b)

(c)

Fig. 4 The result of Gabor filtering: (a) ROI from original mammogram, (b) the map with the maximum values of amplitude M(x, y) and (c) the map with the dominant angles of texture orientation Q(x, y)

the map M(x, y) is thresholded with T1 = 0.75 ∗ AMAX , where AMAX - the maximum value of amplitude in mammogram. We expect that in the blocks (K × K) the calculated histogram of map Q(x, y) (Fig. 5) for ADs should show several dominant peaks (correlating with the dominant texture orientation angles). For normal tissue

Fig. 5 The exemplary histograms of map Q(x, y) for blocks 100 × 100 pixels with normal breast tissue and with architectural distortion

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one dominant peak is expected. Performing histogram analysis of Q(x, y) we utilize threshold T2 to eliminate texture orientation angles with low recurrence number. Additionally, any dominant direction in mammogram texture can be visible on histogram of blocks (K × K) as several near-lying peaks which values are averaged when form sequence is longer than threshold value T3 . Finally, the “probability map ”(Fig.6b) is created by assignment the highest probability of ADs appearance (reflected as a maximum gray scale value MAX) to blocks, in which after the histogram analysis the number n peaks (n dominant angles) is equal or higher than the characteristic number N (established experimentally). For the other blocks the scale is extended as follows: (n ∗ MAX)/N. Next, the blocks with the highest probability of ADs appearance are marked with stars (Fig.7).

Fig. 6 The result of Gabor maps histogram analysis: (a) original mammogram with AD and (b) the “probability map”. The marked circle indicates the sites of AD, detected by radiologist

3.2 DD Method Our DD method (differential directions method) of ADs recognition in selected ROIs consists of three steps: i) directional transform, using 2D Fourier transform in polar coordinates, ii) extraction (with reduction) of features and iii) features classification (Fig. 2). Gabor filtering assigns the local texture orientation. We apply the other texture orientation extractor (including whole region of interest) to acquire the

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Fig. 7 The finally results of GF method: (a) thresholded “probability map”and (b) the output image with marked by stars sites of potential ADs. AD is correctly detected (in the marked circle). The high number of false positives is re reduced in the second stage - DD method.

high directional resolution. We use the directional transform in order to enhance only strong ADs spicules (Fig. 8). To this effect, the 2D Fourier transform in polar

Fig. 8 Schema of directional transform, using 2D Fourier transform in polar coordinates

coordinates is computed using first Radon transform of selected by GF method ROI f (x, y): pφ (x ) =

∑

(x,y)∈φ

f (x, y) = ∑ f (x cos φ − y sin φ , x sin φ + y cos φ ) y

(2)

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where x = x cos φ + y sin φ and y = −x sin φ + y cos φ . We receive the projections pφ (x ) as the sum of f (x, y) values along definite direction (the line at the angle φ ). However, in order to define frequency characteristic of analyzed object (potential AD) along definite direction, 1D Fourier transform pφ (x ) has to be computed for each projection: F{pφ (x )} ≡ Pφ (ω ) = ∑ pφ (x ) exp(−iω x )

(3)

x

substituting equation (2): Pφ (ω ) = ∑ ∑ f (x cos φ − y sin φ , x sin φ + y cos φ ) exp(−iω x )

(4)

x y

1D Fourier transform of projection pφ (x ) is equivalent to transformation of f (x, y) in angular and frequency domain: Pφ (ω ) = ∑ ∑ f (x, y) exp(−iω (x cos φ + y sin φ ))

(5)

Pφ (ω ) = F{ f (x, y)|φ } = F(ωx , ωy )|φ = F(ω , φ )

(6)

x

Therefore,

y

where F(ω , φ ) - the expected 2D Fourier transform in polar co-ordinates. To receive complete directional characteristic of analyzed ROI (for all 180 angles φ ), the mean of |F(ω , φ )| by ω = 1, ..., M has to be calculated in two manners: • the mean of |F(ω , φ )| (Fig. 9): |S1 (φ )| =

1 |F(ω , φ )| M∑ ω

(7)

• the mean of |Fr (ω , φ )| with soft thresholding of |F(ω , φ )|, defined as follows: |Fr (ω , φ )| = 0 < r(φ ) |Fr (ω , φ )| = |F(ω , φ )| − r(φ ) > r(φ )

(8) (9)

where r(φ ) = M1 ∑ω |Ft (ω , φ )| is calculated for each projection. The angular spectrum |S2 (φ )| seems to be more effective for mammograms: |S2 (φ )| =

1 |Ft (ω , φ )| M∑ ω

(10)

For assigned angular spectrum |S(φ )| 13 directional features are extracted, including: • the features based on gray-level co-occurrence matrix (GCM) for α = 0◦ [19]: contrast, correlation, energy, entropy, homogeneity;

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Fig. 9 Two created phantoms: (a) phantom of normal breast tissue - with one lines direction and (b) phantom of AD - with chosen four lines directions. (c) The angular spectrum |S1 (φ )| of two phantoms.

• the statistic features: variance, standard deviation, kurtosis, skewness, energy, entropy • two features computed using approximation of angular spectrum (slope and point of intersection with y-axis). Additionally, to better ADs recognition image features of selected ROI are extracted: i)the features based on GCM for α = 0◦ , 45◦ , 90◦ , 135◦ and ii) the statistic features including also central moments. As the criterion of image features reduction (to assess the significance of every feature for separating two labeled groups: AD or normal tissue) we set area between the empirical receiver operating characteristic curve and the random classifier slope. We normalize the features values and utilize the correlation between features values. The support vector classifier with linear kernel and regularization (from MATLAB toolbox - PRTools4 [12]) is used to classification.

3.3 Results of ArDist Method Our database of mammograms containing ADs consists of 33 images from digital database DDSM (image resolution 43.5 - 50um) [6]. We achieved the sensitivity of GF method equal 79% (26 cases of ADs are detected) at the number of false positives per image FPI = 7.8 (Table 1). The sensitivity of GF method is worse than the model method [14] at the same number of FPI, but it is worth underling fact that the computational complexity of GF method is much lower than the model method. However, the number of false positives was unacceptable. We achieved 292 ROIs (including 34 ROIs with ADs - in one case AD has been marked by two stars). In order to recognize ROIs with ADs DD method is used. To reduce an influence of training and classifying data on classification results was necessary a

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cross validation. The acceptable result of classification was gained for selected 10 image features of low-pass and then high-pass filtered ROIs and all 13 direction features of angular spectrum. As the finally result, we achieved the sensitivity of 86% and the specificity of 89% (Table 1).

Table 1 Efficiency of GF, DD and ArDist method Method

Sensitivity

FP/image or Specificity ∗

GF Method DD Method ArDist Method

79% 86% 68%

0.78 89% 0.86

∗

FP/image (the number of false positives per image) - in GF and ArDist method; specificity - DD method.

Table 2 Comparison between ArDist method and commercial CAD systems Detection Method

Number of images

Sensitivity

FP/image∗

ArDist Image Chacker R2 CADx Second Look

33 45 45

68% 49% 33%

0.86 0.7 1.27

∗

FP/image (the number of false positives per image)

Final result of our ArDist method is promising. The sensitivity of ArDist method amounts to 68% at FPI = 0.86. In comparison with the commercial CAD systems we achieved the higher sensitivity at the comparable number of FPI (Table 2). However, it is necessary to underline databases variety.

4 Conclusion Our ArDist method gives promising results and seems to have high capability to aid radiologists in their work, but method parameters were fitted experimentally to optimize algorithm for concrete data set. More general, adaptive procedures are necessary to conclude the results more reliably. Moreover, in the future research we should improve our ArDist method by adjusting the parameters of Gabor filter to expected features of ADs. Next, the better directional features for improved differentiating ADs from normal tissue of breast are searched. Scalable, two dimensional transforms with nonseparable, flexible kernels are planned to be considered. Families of countourlets, curvelets, beamlets etc. are potentially useful for further ADs detection enhancement.

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References 1. Ayres, F.J., Rangayyan, R.M.: Characterization of architectural distortion in mammograms. IEEE Engineering in Medicine and Biology Magazine (2005) 2. American College of Radiology (ACR): Breast Imaging Reporting and Data System BIRADS, 3rd edn. American College of Radiology (1998) 3. Bird, R.E., Wallace, T.W., Yankaskas, B.C.: Analysis of cancers missed at screening mammography. Radiology 184, 613–617 (1992) 4. Birdwell, R.L., Bandodkar, P., Ikeda, D.M.: Computer aided detection with screening mammography in a University Hospital Setting. RSNA 236, 451–457 (2005) 5. The CADx Second Look system, http://www.icadmed.com 6. University of South Florida: Digital Database for Screening Mammography (DDSM), Florida, USA, http://marathon.csee.usf.edu/Mammography/Database.html 7. Dziukowared, J. (red.): Mammografia w diagnostyce raka sutka, Warszawa (1998) 8. Guo, Q., Shao, J., Ruiz, V.: Investigation of support vector machine for the detection of architectural distortion in mammographic images. Journal of Physics: Conference Series 15 (2005) 9. Ichikawa, T., Matsubara, T., Hara, T., Fujita, H., Endo, T., Iwase, T.: Automated detection method for architectural distorion areas on mammograms based on morphological processing and surface analysis. In: Medical Imaging: Image Processing, vol. 5370 (2004) 10. Koronacki, J., Cwik, J.: Statystyczne metody uczace sie. Akademicka Oficyna Wydawnicza EXIT. Wydanie drugie, Warszawa (2008) 11. Orel, S.G., Kay, N., Reynolds, C., Sullivan, D.C.: BI-RADS categorization as a predictor of malignancy. Radiology 211, 845–850 (1999) 12. Duin, R.P., Juszczak, P., Paclik, P., Pekalska, E., de Ridder, D., Tax, D.M.J., Verzakov, S.: PRTools 4 - A MATLAB Toolbox for Pattern Recognition. Version 4.1, Delft University of Technology (2007) 13. The R2 Technology’s Image Checker, http://www.r2tech.com 14. Rangayyan, R.M., Ayres, F.J.: Gabor filters and phase portraits for the detection of architectural distortion in mammograms. In: Medical and Biological Engineering, pp. 883– 894. Springer, Heidelberg (2006) 15. Rangayyan, R.M., Prajna, S., Ayres, F.J., Leo Desautels, J.E.: Detection of architectural distortion in prior screening mammograms using Gabor filters, phase portraits, fractal dimension and texture analysis. Int. J. CARS (2008) 16. Sampat, M.P., Markey, M.K., Bovik, A.C.: Computer-aided detection and diagnosis in mammography. IEEE Publication, Los Alamitos (2004), e.sharif.edu/~miap/Files/MammographyReview1.pdf 17. Sampat, M.P., Whitman, G.J., Markey, M.K., Bovik, A.C.: Evidence based detection of spiculated masses and architectural distortions. In: SPIE, Medical Imaging: Image Processing, vol. 5747, pp. 26–37 (2005) 18. Schneider, M.A.: Better detection: Improving our chances. Digital mammography. In: Proc. of the 5th Int. Workshop on Digital mamography, pp. 3–6. Medical Physics Publishing, Toronto (2000) 19. Zielinski, K.W., Strzelecki, M.: Komputerowa analiza obrazu biomedycznego. Wstep do morfometrii i patologii ilosciowej. PWN, Warszawa - Lodz (2002)

An Instrument for Monitoring Inflow and Washout of an Optical Contrast Agent into the Brain ˙ Daniel Milej, Michał Kacprzak, Norbert Zołek, Piotr Sawosz, Roman Maniewski, and Adam Liebert

Abstract. A time resolved method based on near infrared spectroscopy for monitoring of changes in tissue absorption and concentration of the exogenoeus chromophore concentration is presented. We constructed a setup which can be used to measure changes in oxygenation of the brain tissue by monitoring of diffuse reflectance at two wavelengths. Currently, the instrument has been modified in such a way that simultaneous measurements of diffuse reflectance and fluorescence can be carried out. We present results of measurement of diffuse reflectance and fluorescence during injection of an optical contrast agent in healthy volunteer.

1 Introduction Methods used routinely in clinical evaluation of structure and function of human brain like computed tomography (CT), magnetic resonance imaging (MRI), and positron emission tomography (PET) are sophisticated and expensive. Moreover, their use require the transport of the patient to the brain imaging facility. Optimally, the method used in brain monitoring should allow to perform measurements at the bedside of the patient. It should be possible to use the method intraoperatively as well. Near infrared spectroscopy (NIRS) [1, 2] is an optical non-invasive method which may fulfil these requirements. This technique is based on assessment of changes in oxy- and deoxyhemoglobin by analysis of changes in attenuation of light measured at several wavelengths and utilization of differences in spectral properties of hemoglobins in near infrared wavelength region. The method can be also applied for assessment of perfusion of human brain by combined application of NIRS technique and the injection of optical contrast agent. Indocyanine green (ICG) is a dye ˙ Daniel Milej · Michał Kacprzak · Norbert Zołek · Piotr Sawosz · Roman Maniewski · Adam Liebert Institute of Biocybernetics and Biomedical Engineering, Polish Academy of Sciences, 4. Ks. Trojdena Str., 02-109 Warsaw, Poland e-mail: [email protected] E. Pi˛etka and J. Kawa (Eds.): Information Technologies in Biomedicine, AISC 69, pp. 85–90. c Springer-Verlag Berlin Heidelberg 2010 springerlink.com 

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which have high absorption in near infrared spectral region, is relative non-toxic [3] and it can be safely injected intravenously in patients. The dye found application in several fields of medicine [4, 5, 6, 7, 8, 9]. In experiments carried out on animals it was shown that ICG allows for evaluation of cerebral blood volume [10]. For monitoring of the inflow and washout of the dye different optical techniques can be applied: (i) continuous wave spectroscopy [11, 12], (ii) frequency domain technique [13] and (iii) evaluation of broadening of picosecond laser pulse during its penetration through the tissue [14, 15]. In recent publications, it was reported that fluorescence light from ICG can be excited with the use of near infrared light during circulation of the dye in the human brain. This light can be detected on the surface of the head using the time-resolved optical setup [16, 17]. Theoretical analysis of light propagation show that changes of moments of distributions of times of arrival of fluorescence photons can be explained considering faster inflow of the ICG to the intracerebral brain tissue and delayed inflow to extracerebral overlaying tissue layers (skin, skull) [18, 19].

2 Methods The constructed setup allows for simultaneous measurement of distributions of times of flight of diffusely reflected photons and times of arrival of fluorescence photons. Single channel of that setup is schematically presented in Fig. 1. Technical details of the setup were presented in more detail elsewhere [20]. The setup is equipping with a semiconductor laser heads operating at a wavelength of 760 nm which allowed to excite fluorescence of the dye. The laser light

Fig. 1 Diagram of the measurement system during the in-vivo experiments

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is delivered to the surface of the tissue with the use of four optical fibers. The light remitted from the medium is transmitted to the photodetectors with the use of four bifurcated fiber bundles. The acquisition of distributions of times of flight of photons is carried out with the use of photomultiplier tubes and eight time correlated single photon counting (TCSPC) PCI cards divided into four reflectance and four fluorescence channels. Appropriate filters applied in each channel allow to easily configure the system for measurement of distributions of times of flight (DTOF) of diffusely reflected photons and distributions of times of arrival (DTA) of fluorescence photons. Additionally, in all channels rotating film filters were applied which allow to adjust intensity of light transmitted to the photodetectors. The TCSPC cards were mounted in an industrial PC. During data analysis, statistical moments, i.e., number of photons, mean time of flight and variance of the DTAs and DTOFs were calculated. For fixation of the source fibers and detecting boundless a flexible pad made of thermoplastic material and plastic foam was used (see Fig. 2). The distance between source fiber position and detection bundle was fixed at 3 cm for all source-detector pairs. For this source-detector separation the laser light may penetrate for the depth of 1.5 cm, i.e. it reaches the cortex of the brain.

Fig. 2 Optode fixation on both sides of the head

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3 Results Example of signals measured in-vivo in a healthy volunteer in diffuse reflectance and fluorescence channels is presented in Fig. 3. Changes in number of photons N/N0 and mean time of flight < t > are presented. In both signals change is clearly visible at the moment of appearance of the dye in the volume between source and detector. Larger amplitudes of changes can be noted in fluorescence channel. Specific changes of the mean time of flight of DTA of florescence photons were noted. This pattern, consisting of early increase of < t > was reported previously and explained by theoretical analysis of the fluorescence light excitation and propagation in layered optically turbid medium.

4 Discussion and Conclusions In this paper we present construction of an optical setup for simultaneous measurement of time-resolved diffuse reflectance and fluorescence. The instrument allows to measure optical signals at 4 spots on every hemisphere of the brain. The aim of further development is to construct an instrument which will be mobile and simple in operation. Laboratory tests on physical phantoms of the tissue [21] and preliminary in-vivo tests confirmed potential effectiveness of the technique in clinical brain assessment. The setup can be potentially easily re-configured for double-wavelength operation, monitoring of diffuse reflectance or fluorescence or combination of these quantities. Development of optimal procedure for fixation of the optodes on the head

Fig. 3 Changes in number of photons N/N0 and mean time of flight < t > of diffusely reflected photons and times of arrival of fluorescence photons obtained during in-vivo experiment. Injection of the ICG at t = 0.

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still remains a serious challenge. The distribution of the fibers and bundles on the surface of the patient’s head must be well defined and size of the optode holder must fit to different shapes of the skulls. Additionally, it should be possible to fix and adjust the optodes on the head in very fast way. Acknowledgements. The studies have been financed by Polish Ministry of Science and Higher Education – research project 3 T11E 01530 and Polish-German project entitled: Hypo- and hyperperfusion during subacute stroke.

References 1. Jobsis, F.F.: Noninvasive, infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameters. Science 198(4323), 1264–1267 (1977) 2. Villringer, A., Chance, B.: Non-invasive optical spectroscopy and imaging of human brain function. Trends In Neurosciences 20(10), 435–442 (1997) 3. Hope-Ross, M., et al.: Adverse reactions due to indocyanine green. Ophthalmology 101(3), 529–533 (1994) 4. de Liguori Carino, N., et al.: Perioperative use of the LiMON method of indocyanine green elimination measurement for the prediction and early detection of posthepatectomy liver failure. Eur. J. Surg. Oncol. (2009) 5. Ishizawa, T., et al.: Real-time identification of liver cancers by using indocyanine green fluorescent imaging. Cancer 115(11), 2491–2504 (2009) 6. Sheng, Q.S., et al.: Indocyanine green clearance test and model for end-stage liver disease score of patients with liver cirrhosis. Hepatobiliary Pancreat. Dis. Int. 8(1), 46–49 (2009) 7. He, Y.L., et al.: Measurement of blood volume using indocyanine green measured with pulse-spectrophotometry: its reproducibility and reliability. Crit. Care Med. 26(8), 1446– 1451 (1998) 8. Ishihara, H., et al.: Does indocyanine green accurately measure plasma volume early after cardiac surgery? Anesth. Analg. 94(4), 781–786 (2002) (table of contents) 9. Guenette, J.A., et al.: Human respiratory muscle blood flow measured by near-infrared spectroscopy and indocyanine green. J. Appl. Physiol. 104(4), 1202–1210 (2008) 10. Leung, T.S., et al.: A new method for the measurement of cerebral blood volume and total circulating blood volume using near infrared spatially resolved spectroscopy and indocyanine green: application and validation in neonates. Pediatr. Res. 55(1), 134–141 (2004) 11. Terborg, C., et al.: Bedside assessment of cerebral perfusion reductions in patients with acute ischaemic stroke by near infrared spectroscopy and indocyanine green. J. Neurol. Neurosurg. Psychiatry 75(1), 38–42 (2004) 12. Keller, E., et al.: Noninvasive measurement of regional cerebral blood flow and regional cerebral blood volume by near-infrared spectroscopy and indocyanine green dye dilution. Neuroimage 20(2), 828–839 (2003) 13. Steinbrink, J., et al.: Relevance of depth resolution for cerebral blood flow monitoring by near-infrared spectroscopic bolus tracking during cardiopulmonary bypass. J. Thorac Cardiovasc. Surg. 132(5), 1172–1178 (2006) 14. Liebert, A., et al.: Time-resolved multidistance near-infrared spectroscopy of the adult head: intracerebral and extracerebral absorption changes from moments of distribution of times of flight of photons. Applied Optics 43(15), 3037–3047 (2004)

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15. Liebert, A., et al.: Bed side assessment of cerebral perfusion in stroke patients based on optical monitoring of a dye bolus by time resolved diffuse reflectance. Neuroimage 24(2), 426–435 (2005) 16. Steinbrink, J., et al.: Towards noninvasive molecular fluorescence imaging of the human brain. Neurodegener. Dis. 5(5), 296–303 (2008) 17. Liebert, A., et al.: Non-invasive detection of fluorescence from exogenous chromophores in the adult human brain. Neuroimage 31(2), 600–608 (2006) 18. Liebert, A., et al.: Monte Carlo algorithm for efficient simulation of time-resolved fluorescence in layered turbid media. Opt. Express 16(17), 13188–13202 (2008) 19. Liebert, A., et al.: Bed side assessment of cerebral perfusion in stroke patients based on optical monitoring of a dye bolus by time resolved diffuse reflectance. Neuroimage 24(2), 426–435 (2005) 20. Kacprzak, M., et al.: Time-Resolved Optical Imager for Assessment of Cerebral Oxygenation. Journal of Biomedical Optics 12, 034019 (2007) 21. Milej, D., et al.: Advantages of fluorescence over diffuse reflectance measurements tested in phantom experiments with dynamic inflow of ICG. Opto-electronics Review (2010) (accepted for publication)

4D Segmentation of Ewing’s Sarcoma in MR Images Joanna Czajkowska, Pawel Badura, and Ewa Pietka

Abstract. This paper presents the first stage of a semi-automatic method for the segmentation of nodules of the skeleto-muscular system from magnetic resonance (MR) imaging. The method suggested is efficient irrespective of the tumour location in human body. It is based on Fuzzy C-Means clustering (FCM), Gaussian Mixture Models (GMM) and Fuzzy Connectedness analysis applied to the dataset consisting of T1W and T2W series. In this study a method of transforming the results between planes is also presented. The suggested algorithm has been evaluated on the examinations of different parts of the body, where Ewing’s sarcomas have been indicated by a radiologist.

1 Ewing’s Sarcoma Segmentation Problem Ewing’s sarcoma is a highly malignant tumour usually found in children and young adults [1]. It occurs in bone tissue and it may also spread to muscles and soft tissues surrounding the bone. In this study an application is created, that assists the radiologists with comparative analysis of consecutive follow-up MR studies and evaluation of tumour size changes. The detection and staging of bone and soft tissue tumours is usually based on T2W images and contrast enhanced T1W images in different planes, both with fat saturation applied. Merging and transposing the results from one plane to another is of great diagnostic value for the radiologists. Fig. 1 shows the examples of the T2W as well as contrast enhanced T1W, fat saturated images. The Ewing’s sarcoma is visible on the pinky in the coronal plane and on the right leg in the axial and coronal planes. It is the high-density area in both imaging series around the shinbone, on the shinbone and on the kneecap. However, the tumour area has different density on the slices, which is the main difficulty in this task. Joanna Czajkowska · Pawel Badura · Ewa Pietka Silesian University of Technology, Akademicka 16 st., 44-100 Gliwice, Poland e-mail: [email protected], [email protected], [email protected] E. Pi˛etka and J. Kawa (Eds.): Information Technologies in Biomedicine, AISC 69, pp. 91–100. c Springer-Verlag Berlin Heidelberg 2010 springerlink.com 

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Fig. 1 An example of T2W (top) and T1W (bottom) MR images with Ewing’s sarcoma visible on the pinky (coronal plane) and the right leg (axial and coronal planes). The arrows indicate the lesion.

Before the image analysis starts, one pixel belonging to the tumour area has to be indicated by the radiologist on any chosen slice and plane. For further stages of the algorithm, it does not matter on which series or slice the pixel will be indicated. It entirely depends on the radiologist’s decision and preferences. The pixel indicated is transformed into all the series and planes. The further analysis is performed simultaneously on both T1W and T2W series in the same plane. Afterwards, on the basis of the kernelised version of the Fuzzy C-Means (FCM) clustering, the region of interest (ROI) is found. It is then divided into three classes using a Gaussian Mixture Model and the class with the highest mean value creates the seed points area for Fuzzy Connectedness (FC) analysis. The fuzzy membership level, which restricts the segmented area, is also calculated on the basis of the FCM clustering. The independent series analysis is followed by multiseries processing. The results previously obtained are transformed from one plane to another. On this basis the new seed points area on the target series is calculated and FC analysis as well as FCM clustering are repeated, yielding the final segmentation results.

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2 ROI Detection, Fuzzy C-Means Clustering FCM is a clustering method based on the minimisation of an objective function [4] [2]. It divides a finite set of elements into k clusters with respect to some given criterion. The number of clusters k is usually predefined. The standard FCM objective function for partitioning a dataset {xi }Ni=1 into k clusters can be written as c

Jβ =

N

β

∑ ∑ uki xi − vk2,

(1)

k=1 i=1

β being a weighted exponent on each fuzzy membership. In each iteration of the FCM algorithm, for each cluster k, the fuzzy cluster centre β

vtk =

∑Ni=1 uki xi

(2)

β

∑Ni=1 uki

is calculated using a membership function U(t) . In the first iteration U(1) is set to random values. In the next steps (t+1)

uki

1

=

2

∑cj=1 (dki /d ji) (β −1)

.

(3)

If U(t+1) − U(t)  ≤ ε , the algorithm is finished and the analysed data xi belongs to the class k with the maximum uki value. However, the algorithm presented above is sensitive to artefacts and noise. The authors of [2] and [3] suggested some modifications, which deal with this problem. One of them - the Kernel based Fuzzy C-Means (KFCM) is used in this work. The algorithm proposed in [3] uses a kernel-induced distance metric to replace the square one applied in FCM. In this modification, the objective function is given as [3] c

Jβ =

N

β

∑ ∑ uki φ (xi ) − φ (vk )2,

(4)

k=1 i=1

where φ is a nonlinear transformation into a higher dimensional feature space F and φ (xi ) − φ (vk ) = K(xi , xi )K(vk , vk ) − 2K(xi, vk ).

(5)

In the software presented, on the basis of the pixel indicated and after the application of the 2D KFCM algorithm, the ROI is found. The pixel intensities in the T1W and T2W series are subjected to the 2D KFCM clustering. Two regions of interest are found. The first one is the 3D bounding box ROI circumscribing the object that includes the selected pixel with its 6-neighbourhood. The second one, denoted as ROIC , includes the object itself (Fig. 2).

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T1W

T2W ROI

ROIc

Fig. 2 ROI detection using the KFCM algorithm. A slice selected from the T2W series (left), the corresponding slice from the T1W series (right) and the clustering result with the ROI found (middle).

3 Gaussian Mixture Model In the following step a clustering method based on the histogram of the ROIC in two whole series, using a 2D Gaussian Mixture Model (GMM) with three Gaussian components, is applied. As a result, the seed points are obtained inside the tumour area for a 4D FC analysis described in section 4. The mixture model assumes that each group of the data is generated by a normal probability distribution [4]. The probability density of the mth component is given as 1 1 T −1 p(x/θm ) = √ n (6) 1 exp(− (x − μm ) Cm (x − μm )), 2 2π |Cm | 2

μm denoting the mean values vector and Cm the covariance matrix. For the mixture model with M components in the feature space Rn for n ≥ 1 dimensions M

p(x) = 

∑ αm p(x/m),

(7)

m=1

where αm ∈ [0, 1]( m = 1, 2, ..., M) and M

∑ αm = 1.

(8)

m=1

αm denotes the mixing proportion coefficient. Then, to get θ = (α1 , ..., αM , θ1 , ..., θM ), where θm = (μm , Cm ), equation (7) can be written as follows p(x/θ ) =

M

∑ αm p(x/θm).

(9)

m=1

The model parameters are estimated by the expectation maximisation (EM) algorithm [4].

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As a result the ROIC is divided into three subregions (Fig. 3). The subregion with the highest values in the mean values vector makes up the seed points for the next processing step. The mixture parameters calculated for this subregion, namely the covariance matrix C and the mean values vector M = {μ1 , μ2 }, are also used in the following step.

KFCM

GMM

seed points area

Fig. 3 Seed points selection. KFCM clustering results (left). Subregions obtained with GMM clustering (middle). Seed points area selected (right).

4 Fuzzy Connectedness The Fuzzy Connectedness (FC) analysis focuses on fuzzy relations between two image points1 . Specifically, a mutual and symmetric relation called fuzzy affinity μκ (c, d) ∈ 0, 1 connects two neighbouring points, ie. is nonzero only if c and d are spatially adjacent (here, the hard 3D 6-adjacency relation is used). Several forms of the fuzzy affinity function have been discussed [5, 7], most of them taking the intensities f (c) and f (d) of c and d as arguments. The value of μκ may depend on either the mean intensity or the absolute difference between f (c) and f (d), according to

μκ (c, d) = μα (c, d) · g(μφ (c, d), μψ (c, d)),

(10)

where μα stands for a spatial adjacency relation, and g(·) is a function of the mean intensity based (μφ ) and intensity gradient based (μψ ) affinity components. In this study a multifeature approach has been proposed. As mentioned above, two corresponding series, namely T1W and T2W, are taken into consideration. Each point c under FC investigation is then described by two features: f1 (c) and f2 (c), being its intensities in both series. Fuzzy affinity function takes advantage of four intensities, two of them describing each of the points c and d. In this study only the mean intensity component is considered, which leads to 1

More details can be found in [5, 6].

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μκ (c, d) = μα (c, d) · e− 2 (f−M)

T C(f−M)

,

(11)

where each value of the vector f and of the mean intensity vector M relates to a single series ⎡ ⎤ ⎡ ⎤ f 1 (c)+ f 1 (d) μ1 2 ⎢ ⎥ ⎣ ⎦. f=⎣ , M = ⎦ f 2 (c)+ f 2 (d) μ2 2

The μ1 , μ2 and C parameters are obtained from the GMM step. At the preprocessing step the images are prepared for the FC analysis. The pixel intensities f1 and f2 above the mean values μ1 and μ2 , respectively, are replaced with the corresponding mean value. The body of the FC algorithm remains unchanged [8]: the FC scene is computed in a 3D space over the GMM-selected seed points. The Dijkstra’s algorithm is used after setting the affinity values to 1 for all the seed points. A slice chosen from the fuzzy affinity scene is shown in Fig. 4 (left). The fuzzy affinity value restricting the finally segmented area is calculated on the basis of FCM clustering with two clusters (Fig. 4).

Fig. 4 Results of the fuzzy connectedness analysis for a chosen slice (left). Thresholding on the basis of the FCM algorithm (middle). Final segmentation results (right).

5 Transformation During a single MR examination, several series are typically acquired (e.g. T1W, T2W, contrast enhanced T1W, etc.) in three basic planes: axial, sagittal and coronal. In radiological assessment all these series may be relevant for the final diagnosis. For the analysis of the whole examination the indirect transformation T is employed. First, all the already segmented points are transformed into the target series, using DICOM positioning information [9]

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Transformation

Erosion

AND

Fig. 5 An example of transformation and new seed points selection

P. - the coordinates of the voxel (i,j) in the frame’s image plane in units of [mm]. S. the three values of the Image Position (Patient) (0020,0032) attributes. It is the location in mm from the origin of the RCS. X. - the values from the row (X) direction cosine of the Image Orientation (Patient) (0020,0037) attribute. Y. - the values from the column (Y) direction cosine of the Image Orientation (Patient) (0020,0037) attribute. i, j - column and row index to the image plane. Δ i, j - column or row pixel resolution of the Pixel Spacing (0028,0030) attribute in units of [mm].2 2

More details about the DICOM coordinate system can be found in [9].

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Fig. 6 Results of a single plane multiseries analysis in the axial plane (upper left). Results of a single plane multiseries analysis in the coronal plane (upper right). Results of a multiplane multiseries analysis in the coronal plane (bottom). The arrows indicate the false positives.

The transformation is defined in such a way that it maps the 3D row-column-slice (RCS) space into a 3D xyz space Pxyz = PRCS · T.

(12)

Multiple series can be transformed into the same xyz coordinate system. With the inverse transformation T −1 the mapping from one series into another may be performed by using this xyz coordinate system. The steps described in sections 2, 3 and 4 are independently performed for all the planes. The results of applying the FC step are transformed to the desired plane from the other planes. Next, the transformed masks are subjected to morphological erosion and the common area of the resulting masks and the mask originally obtained in the desired plane is found (Fig. 5). The new seed points area is thus obtained for

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Fig. 7 Final results - a 3D view

a renewed FC analysis (as described in section 4), yielding the final tumour areas mask. A comparison of results obtained for single plane and multiplane processing is shown in Fig. 5.

6 Results Studies of two patients have been used for the initial evaluation of the suggested algorithm. The analysed Ewing’s sarcomas arose in two different parts of the body. Each of the studies consists of T1W and T2W series, in two planes, the series containing between 10 and 30 slices. The series also differ in the size of images. In total 134 images have been analysed. Each study was earlier described by a radiologist. The achieved segmentation results (Fig. 5) are comparable to those obtained by a doctor. All the tumour areas are included in the segmented regions. However, in some cases false positive areas appeared. They constitute at most 5% of the whole volume of the segmented structure. It should be underlined that the testing results are repeatable. Moreover, from medical point of view, an over 20% change in the volume of tumour tissue between subsequent examinations is relevant. The obtained 5% accuracy will thus not hinder the diagnosis. Furthermore, the CAD workstation will enable the user to remove semi-automatically these regions from the segmented areas.

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J. Czajkowska, P. Badura, and E. Pietka

7 Conclusions An effective method for semi-automated 4D segmentation of Ewing’s sarcoma tumours has been presented. FCM clustering, its kernelised version, GMM analysis and FC algorithm have been used. The two different planes coming from one examination are combined on the basis of DICOM header information. The segmentation method has been tested on medical examinations and consulted with a radiologist. The results obtained are satisfactory, which encourages to further develop this method. As a result, the efficiency of the suggested algorithm should enhance. It is also planned to use this methodology in the segmentation of other types of cancer and anatomical structures. The CAD workstation will assist radiologists in the diagnosis and could also be useful for education and training.

References 1. University of California, San Francisco Children’s Hospital, Medical Service, Sarcomas, http://www.ucsfhealth.org/childrens/medical_services/ cancer/sarcomas/conditions/ewings/signs.html 2. Chen, S., Zhang, D.: Robust Image Segmentation Using FCM With Spatial Constraints Based on New Kernel-Induced Distance Measure. IEEE Transactions on Systems, Man and Cybernetics-part B, Cybernetics 34(4) (August 2004) 3. Zhang, D.-g., Chen, S., Pan, W.-S., Tan, K.-R.: Kernel-Based Fuzzy Clustering Incorporating Spatial Constrains for Image Segmentation. In: Proceedings of the IMCL 2003, Wan, November 2-5 (2003) 4. Mekhalfa, F., Goumeidane, A.B.: Unsupervised Algorithm for Radiographic Image Segmentation Based on the Gaussian Mixture Model. In: EUROCON 2007 Int. Conf. on Computer as a Tool, Warsaw, September 9-12 (2007) 5. Udupa, J., Samarasekera, S.: Fuzzy connectedness and object definition: Theory, algorithms, and applications in image segmentation. Graphical Models and Image Processing 58(3), 246–261 (1996) 6. Udupa, J., Saha, P.: Fuzzy connectedness and image segmentation. Proceedings of the IEEE 91, 1649–1669 (2003) 7. Saha, P., Udupa, J., Odhner, D.: Scale-Based Fuzzy Connected Image Segmentation: Theory, Algorithms, and Validation. Computer Vision and Image Understanding 77(9), 145–174 (2000) 8. Badura, P., Pietka, E.: Semi-Automatic Seed Point Selection in Fuzzy Connectedness Approach to Image Segmentation. Advances in Soft Computing: Computer Recognition Systems 2(45), 679–686 (2007) 9. Digital Imaging and Communications in Medicine standard. http://medical.nema.org/ (Cited February 11, 2010)

Segmentation of Stained Lymphoma Tissue Section Images Urszula Neuman, Anna Korzynska, Carlos Lopez, and Marylene Lejeune

Abstract. In order to obtain supporting tool for the pathologists who are investigating prognostic factors in folicular lymphoma a new method of color images segmentation is proposed. The method works on images acquired from immunohistochemically stained thin tissue sections of lymph nodes coming from patients with folicular lymphoma diagnosis. The proposed method of segmentation consists of: pre-processing, adaptive threshold, watershed segmentation and post-processing. The method is tested on a set of 50 images. Its results are compared with results of manual counting. It has been found that difference between the traditional method results and the proposed method is small for images with up to 100 nuclei while in more complicated images with more then 100 nuclei and with nuclei clusters this difference increases.

1 Introduction Lymphoma is a cancer caused by an abnormally fast proliferation of lymphoid cells. There are more than 20 different types of lymphoma cancer, more or less aggressive [1]. In the current practice of pathology, the identification of specific clinical markers and particular molecular alterations represents an indispensable routine for diagnostic, predictive and therapeutic purposes. Follicular lymphoma (FL) is the prototype of indolent lymphoma characterized by long median survival, even without therapy, and rare spontaneous remissions. The inconsistency of the disease Urszula Neuman · Anna Korzynska Nalecz Institute of Biocybernetics and Biomedical Engineering, PAS, ul. Ksiecia Trojdena 4, 02-109 Warszawa, Poland e-mail: [email protected] Carlos Lopez · Marylene Lejeune Molecular Biology and Research Section, Hospital de Tortosa Verge de la Cinta, C/ Esplanetes 14, Tortosa 43500, Tarragona, Spain e-mail: [email protected] E. Pi˛etka and J. Kawa (Eds.): Information Technologies in Biomedicine, AISC 69, pp. 101–113. c Springer-Verlag Berlin Heidelberg 2010 springerlink.com 

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course makes it difficult to gain a clear consensus about the usefulness of the different treatment options proposed for these patients. In the search of new prognostic and predictive factors, different studies have demonstrated that an exclusively genetic model may not be sufficient to explain the pathogenesis of FL. Therefore, other growth and progression supports, like the inflammatory/immune microenvironment response to the tumor, have been proposed. Recent studies have defined follicular regulatory T cells as independent predictors of overall survival in these patients [2, 3, 4]. The T cells seems to be able to reduce tumor-driven immune suppression with clinical benefit for patients. The presence of this specific subset of immune cells with immunosuppressive activities can be detected by the fact that they express a high level of the forkhead transcription factor box protein P3 (FOXP3). Immunohistochemistry (IHC) is a technique for identifying cellular or tissue constituents (antigens) by means of antigen-antibody interactions, the site of antibody binding being identified either by direct labelling of the antibody, or by use of a secondary labelling method. IHC has found numerous applications in medicine, especially in cancer diagnosis and prognosis. Lymphomas are among the cancers that most dependent on IHC for treatment decisions. In the evaluation and quantification of positively immunostained cells, the most prevalent method is the manual counting performed by the pathologist using a conventional microscope. To avoid subjectivity, a number of automated image analysis programs suitable for use in histopathology are recently under investigation of various research groups. Several successful applications of supporting diagnosis,prognosis therapy evaluation processes based on immunohistochomically stained samples using image processing and analysis are reported in prostate [5], glands [6] or cervical [7], breast cancers [8], lymphomas [9] and others neoplasms [10, 11, 12]. Previous results obtained with automated or semi-automated segmentation of immunohistochemically stained digital images have used available commercial programs such as Photoshop [13], Image-Pro Plus [14], Visilog [15] or ACIS [16]. Moreover, due to increase of physicians’ need of evaluating their diagnosis and calculations an internet platform software EAMUS has been arranged. The software is dedicated for general measurement of various features from immunohistochemistry and deals with various stains and colors in images [17]. Many studies, regardless of the type of cancer and affected organs, are related to color space changes and try to find the best space in which a color image segmentation can be performed [18, 19, 20]. Some of them even propose self generated spaces which are constructed as an optimized space to contrast specific colors [21, 22]. The studies give contradictory conclusions about usefulness of various color spaces [23, 24, 25]. Typically a conventional color segmentation is applied to each component of a color space and results are combined in some way to obtain the final result. Study presented in this paper is based on modified B channel from the RGB color space [26]. Some of the methods are based on color-based thresholds or on clustering with fixed number of classes [27, 28]. However, if there is inhomogenity in color and in light distribution across an image one global threshold is not a good solution. In our study an adaptive threshold [29, 30] is used because of big tone variation observed

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in each image and from one image to another. Typically as a result of image segmentation the image maps are constructed. In many studies those maps are processed by morphological operation to obtain final results for example quantification of specific area or objects in the image [21, 17, 31]. Presented in the paper study also uses morphological operations, morphological filtering and watershed [32] to process results and prepare maps to count number of nuclei. Investigation presented in the paper uses Gaussian pyramid [33, 30], which is commonly used in image processing, to reduce size of image. Advantages coming from this method are described further in the text. Digital images of immunohistochemically indirectly stained histological samples prepared to show location and a number of T regulatory cells are used in this paper. Nuclei with positive immunoreactivity against the protein FOXP3 became brown during the staining process due to 3,3’-Diaminobenzidine (DAB). Other nuclei with negative immunoreactivity become blue because of a hematoxilin counterstaining. Details of staining process are described further. The method proposed in this paper localises and counts T regulatory cells (the brown nuclei) inside the neoplastic follicles (in the image).

2 Materials Images of lymphoma immunohistochemically stained tissue differ in tones, number and dispersion of objects. There are two basic sources which amplify the variation in the images: a staining process and the image capturing process. In the staining process the variation is connected with variation of tissue features and humane action variability in processing [34, 35]. While in the image capturing process the variation depends on visual system of a person who acquires the images and properties of microscope and camera used during image capturing. Moreover, even one person can choose various settings depending on his/her mood and trim.

(a) A part of an original image

(b) After color filtering

Fig. 1 Smudges in background: an original image and the image after color filtering

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Each image consists of background, blue stained nuclei and brown stained nuclei. The bright background fills space between nuclei usually with light blue color. In some specimens smudges, which are fragments of positive nuclei destroyed during tissue cutting, can be locally observed in the background (see Fig. 1). These fragments depend of the position of the nuclei in the section and the level of the cut. Color of the smudges is non-uniform, it is bright brown up to yellow mixed sometimes with blue. Blue stained nuclei distribution is very dense and the blue nuclei fill majority of each image area. Size and shape of those nuclei vary in each image. The variation of size comes from fact that spherical and ellipsoidal nuclei are cut into thin slices in various positions. Also the shapes of the blue nuclei in image are changing due to cutting process from round to elongated. Intensity of the blue color is significantly different for the various images, there are both pale (see Fig. 2(a)) and intensively blue images (see Fig. 2(c)). Inside brighter blue nuclei a texture (brighter and darker nucleus fragments) can be observed.

(a) A weak stain

(b) A normal stain

(c) An intensive stain

Fig. 2 Variation of intensity of blue in images of stained specimens

The brown stained nuclei are usually surrounded by the blue nuclei. Distribution of the brown nuclei is usually homogeneous but sometimes in specimens with high density of the brown nuclei, clusters created by several neighbouring cells can be observed. Objects in the clusters are very difficult to segment because they are touching or overlapping. Shapes of the brown nuclei are usually round, sometimes elliptical. A brown nuclei color variation is bigger than blue nuclei color variation observed in one image (see Fig. 2(b)). The brown color can change from bright brown (yellowish or grayish) to near black brown. In the bright brown nuclei a small texture can be observed (see Fig. 2(a)).

3 Methods Task of the proposed algorithm is counting brown color stained nuclei in described above images.

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3.1 Algorithm Description The algorithm consists of: (1) pre-processing, (2) two-level segmentation and (3) post-processing. Pre-processing: Before applying the main segmentation process each image is preprocessed by two consecutive steps: color separation and rescaling.

(a) An original image

(d) Morphological filtering

(b) Color separation

(e) Watershed

(c) Adaptive threshold

(f) Original plus result borders

Fig. 3 The algorithm’s steps

Firstly brown color in an image is separated by replacing with white pixels all the pixels which are out of defined range of brown color (see Fig. 3(b)). The brown color definition has been adjusted experimentally by establishing proper range for each of three color channels from the RGB color space. Unfortunately a dark blue color is included in the defined range of brown color. Shrinking the range in order to eliminate the dark blue color excludes some nuclei with positive colors. Hopefully the blue color nuclei are textured structures and the dark blue structures preserved in an image after color separation are shaped as small spots. Those small spots are removed later using morphological operations. Secondly the image is rescaled with Gaussian pyramid [33, 30]. Size and resolution of the image become 16 times smaller (see Fig. 3(b), upper left, black box). Objects after such rescaling are smooth and compact what is visible in Fig. 3(c). Moreover the time of algorithm proceeding visibly decreases. Two-level Segmentation: In the main segmentation process two steps of image processing are performed. The first step is an adaptive threshold [29, 30] and the second step is a watershed segmentation [36, 37].

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Adaptive Threshold: As it has been earlier described a big tone variation in image and from image to image is observed. The adaptive threshold is flexible and quite resistant to this type of variation so it is introduced in the algorithm. It has been observed that the blue channel of the pre-processed image has the most contrasting boundaries of separate nuclei so the threshold is calculated for this channel. The adaptive threshold uses window - a square (30x30 px) which is moved through the image. For each position of the window the algorithm calculates mean value of pixels (T) and difference between maximal and minimal value (D) in the window. Having D it is possible to decide if the window contains edges. It is assumed that for the value of D smaller than 6% of the maximal possible value of the image (here 255) there are no edges inside the window. If there are no edges the middle point of the window is compared with mean value T and classified as background or foreground. If there are edges inside it is necessary to recognise if the middle point of the window is an object or not. This part of image processing produces a binary map containing white objects on black background (see Fig. 3(c)). Noise, which comes from dark blue spots is removed from the map by morphological opening filter (see Fig. 3(d)). The filter uses disc-shaped strel element with radius 3. Watershed Segmentation: As the white objects in the adaptive threshold map are sometimes related to more then one nuclei the second step of segmentation - watershed [32, 38] is introduced to separate the nuclei. In order to use the watershed as a shape based segmentation a distance transform of the map is calculated [39]. Additionally a morphological reconstruction on the distance transform image is introduced to simplify it and to eliminate small shape disturbances. The morphological reconstruction is made using as markers image which is result of constant value (in our case it is 0.3) subtraction from the distance transform image. So the brightest parts of the distance transform are used as markers [40, 41, 36, 39]. After the reconstruction the distance transform is less complicated and results of its watershed are more proper. The result of the watershed are boundaries of single nuclei (see Fig. 3(e)). The watershed segmentation works very well by separation two round objects connected with "bottle neck" but it has problems with detection of other types of nuclei connections (e.g. tree cells creating flower-shaped object). Post-processing: The last step of the algorithm is increase of the image to the original size using invert Gaussian pyramid. In the Fig. 3(f) rescaled boundaries imposed on an original image are shown. In the Fig. 4 part of other original image with results of the proposed method is shown in a context of the results of traditional counting (Fig. 4(b)). It can be observed that most of the found by the method objects are marked also by an operator, expect of two objects by the border of the image and two shown by the white boxes.

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(a) An original image with results of the pro- (b) Marks on original image made by patholposed method shown as black spots ogist Fig. 4 An original image with results of the proposed method and results of the traditional method

3.2 Algorithm Implementation The algorithm is implemented in MATLAB and C. The most time consuming operations (adaptive threshold) are written in C. The implementation of the algorithm does not have any graphical user interface jet.

3.3 Evaluation of the Proposed Method To evaluate quality and an average time of performance of the proposed algorithm a comparison with a traditional method of counting of nuclei in immunohistochemically stained specimens is made. The traditional quantification of specimens made by pathologists is always subjective but we have no other method at ours command to compare. The traditional method bases on manual counting of visually selected objects. In this paper the manual counting is made interactively with software ImagePro Plus 5.0 which allows operators to mark counted objects with circles. This interactive procedure counts objects marked by operator. To reduce inter observer variability one operator (pathologist) has made the manual calculation three times to obtain an average number of objects for each image and to prepare a counting maps (see Fig. 4(b)). An error of the automatic method for one image is defined as: ERR = (

|AUT O − MAN| ) · 100% MAN

where: ERR - an error of the automatic method, AUTO - a number of nuclei detected by the automatic method, MAN - a reference number from the averaged traditional counting.

(1)

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A mean error of the automatic method is mean value of error obtained for the set of all investigated images. In order to show structure of the error done by the automatic method a correspondence between results of the proposed method and results of the manual counting is examined for 5 chosen images. During this examination not only an absolute difference between the results (ABS) but also elements which creates the error are calculated. To these elements belong: 1. NOV - number of nuclei counted by the pathologist as one object and by the proposed method as more than one, 2. NM - a number of objects found by the method as one object and by the pathologist as more than one nuclei, 3. NEX - a number of objects found by the proposed method but rejected by the pathologist, 4. NUM - a number of nuclei not found by the proposed method but found by the pathologist. The mean time of one image processing is precisely measured by computer while the time of the traditional counting is estimated from notes.

3.4 Sample and Image Acquisition During the method evaluation process a biological material from Hospital ”Verge de la Cinta” in Tortosa prepared by several technicians according a standard procedure is used. They cut a formalin-fixed paraffin- embedded tissue parts into 3μ m thin sections. The section are dried, deparaffinized in xylene, rehydrated in graded ethanol and washed in water and PBS. Antigen retrieval is achieved by heat treatment in pressure cooker or pronase digestion. Samples ware incubated with the appropriate dilution of the primary antibody FOXP3-236A/E7 (monoclonal antibody, Monoclonal Antibodies Unit, CNIO, Madrid, Spain). The immunohistochemical indirect staining is made using a Horizon TechMate (Dako) devise. During the staining process nuclei that have positive immunoreactivity against FOXP3 become brown while all other become blue because of counterstaining with hematoxylin. Staining intensity can change a little bit every day depending of different external factors. Positive and negative controls are introduced every day in the series. One person makes the image acquisition, so there is no error connected with changing of a personal visual system. As the images are taken during several sessions the settings of the camera can change according to external factors like sun or artificial light conditions. Obviously the settings depend on density of tissue and number of brown nuclei in field of the image. A Leica DM LB2 upright light microscope (Leica Microsystems Wetzlar GmbH, Wetzlar, Germany) with a 40x plane apochromatic objective with a numerical aperture of 0.63 and a digital camera Leica DFC320 (Leica Microsystems Digital Imaging, Cambridge, UK) controlled by Leica DFC Twain software 6.3.0

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(Leica Microsystems Digital Imaging) are used during the acquisition process. Size of acquired images is 2088x1550 pixels. Each single pixel corresponds to about 0.5μ m. That means that each image shows 3.8mm x 2.8mm rectangle part of a specimen. According to information from The Hospital in Tortosa up to 293 of nuclei can be expected in one image and the mean value of the number of nuclei is about 65.5± 57.3 [2]. The proposed method has been tested on a randomly chosen set of 55 images coming from The Hospital in Tortosa. 5 of them have been excluded from investigation due to different color ton.

4 Results Results presented in following section had been obtained based on set of 50 images acquired according to the above description. Results of evaluation of the proposed method are shown in two tables. Table 1 compares mean result of the method and mean result of the traditional counting. The table shows also the mean time of one image proceeding. The time of processing of one image is significantly shorter than the time needed for the traditional counting. Table 2 presents correspondence an differences between the results of the proposed method and the results of the traditional counting for 5 chosen images.

Table 1 Mean result of the proposed method versus the mean manual counting Kind of counting

Mean amount of nuclei per image

Mean error [%]

Mean time of one image proceeding

The manual count The proposed method

94 88

11

few minutes 18 sec

Table 2 shows how many objects are classified similarly in bought methods (from 83% to 100%) and how many of them are missclassified. An analyse of those errors is presented in the following section.

5 Discussion Mean error of the proposed method which equals 11% has several sources. In order to investigate a structure of the error the Table 2 is introduced. Images from the Table 2 can be divided into two main groups: ’dense images’ with a number of nuclei more then 100 (last two rows of the Table 2) and ’slack images’ with a smaller number of nuclei (three first rows in the Table 2).

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Table 2 Detailed results obtained for 5 chosen images: IM - an image number, NEQ - a number of nuclei similarly classified by proposed method and by pathologist (given also in percents as reference to the traditional count), other designations in the table columns according to section 3 IM

MAN

AUTO ABS

NEQ

NOV

NM

NEX

NUM

1 2 3 4 5

43 42 31 103 119

42 37 32 119 114

39 (91%) 37 (88%) 31 (100%) 85 (83%) 102 (86%)

2 0 0 20 2

1 0 0 5 4

0 0 0 9 6

2 5 1 0 5

1 5 1 16 5

In the ’slack images’ the main source of error are the nuclei undetected by automated method. It is caused by the variation of image color tone. The results obtained from the image 1 (first row of the Table 2) show that sometimes absolute difference gives lower error then it really is. In this case the number of over-segmented nuclei is compensate with the number of under-segmented objects containing more than one nucleus. The ’dense images’ are hard to segment. The number of objects with extra segments and the number of objects which consist of more then one nucleus are significant. As mentioned in section Images Characteristic in ’dense images’ brown nuclei touch and overlap forming clusters which are difficult to divide into single nuclei. The watershed segmentation works well for groups of nuclei forming long ribbons but for other shapes of clusters it produces incorrect segmentation but overall error is still in acceptable range. The traditional counting is especially hard in case of ’dense images’ so the manual counting results are less reliable then for images with small number of nuclei.

6 Conclusions The results show that the proposed method can be useful in supporting of a pathologist, because the difference between the traditional method results and the proposed method results is small for ’slack images’ while in more complicated ’dense images’ with nuclei clusters this difference increases. Automated image analyses save time consumed by boring counting of nuclei and decrease intra and inter operator variability in nuclei counting. Using proposed method physicians would concentrate on an examination of the other features needed to take decision about patient treatment. In further work precision and accuracy of the method should be increased. It will be obtained by adding to the method unification of range of image tone and by preparing a special procedure for the most difficult nuclei clusters to divide it into single nuclei. It is supposed that the information about the tissue structure which is available from the histological thin section can be helpful in solution of the cluster problem.

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Anterior and Posterior Cruciate Ligament – Extraction and 3D Visualization Piotr Zarychta and Anna Zarychta-Bargieła

Abstract. This paper shows successive steps in extraction and 3D visualization process of both anterior and posterior cruciate ligaments. In the first stage a region of interest including cruciate ligaments (CL) is outlined. The automatic method of location of the CL on the T1W MR knee images is based on fuzzy C-means (FCM) algorithm with median modification. The next step of that process is an extraction of the cruciate ligament structure using the fuzzy connectedness approach. In the last stage a 3D structures of the anterior cruciate ligament and posterior cruciate ligament are built. These spatial structure is created through layer composition of the base images by using a linear interpolation.

1 Introduction Anterior and posterior cruciate ligaments (ACL and PCL) are main stabilizers of the knee joint in the sagittal plane. Likewise, they contribute to the stabilisation in two remaining plans: coronal and transverse. Cruciate ligaments (CL) together with the shape of articular surface, muscles and contact forces ensure proper arthrokinematics. They play an important role in both active and passive motion. During active motion CL resist translations and reduce shear forces, whereas during passive motion CL help to change rolling into sliding movements [1]. The amount of forces loading the ligaments depends of actual knee position, knee moment and tibiofemoral joint compression forces. During open kinetic chain extension ACL strain increases while flexion angle decreases (from 40◦ of flexion). The bigger knee extension moment, the higher is ACL strain. During open kinetic chain flexion PCL Piotr Zarychta Silesian University of Technology, Akademicka 16 st., 44-100 Gliwice, Poland e-mail: [email protected] Anna Zarychta-Bargieła Hospital in Dabrowa ˛ Górnicza, ul. Szpitalna 13, 41-300 Dabrowa ˛ Górnicza, Poland E. Pi˛etka and J. Kawa (Eds.): Information Technologies in Biomedicine, AISC 69, pp. 115–122. c Springer-Verlag Berlin Heidelberg 2010 springerlink.com 

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Fig. 1 T1W MR series - signal from data base clinical hospital

strain increases rapidly above 30◦ and reaches the maximum above 90◦ of flexion. In closed kinetic chain motion (like sqatting), tibio-femoral joint compression forces and contraction of muscles stabilising the joint, reduce shear forces and decrease ligament strain. Cruciate ligaments control rotational movements in the flexed knee and together with collateral ligaments ensure rotational stability of the extended knee [4]. For that reason cruciate ligaments belong to the group of anatomical structures, which are frequently susceptible to injuries, especially in the athletes. Ligamentous injuries of the knee are a very important and complex medical problem. The manual examination and after that the MR methods remain the basic approach to the injured knee. Appositely performed clinical evaluation plus additional MR slices of the knee joint determine the proper clinical way and gives information about therapy should be ordered. The MR series of the knee joint have two elementary advantages: the first precise level of knee insufficiency and the second make possible extracting and next show a three-dimensional cruciate ligament model. In this study a segmentation methodology has been developed, that extracts the anterior and posterior cruciate ligaments from T1W MR series (Fig. 1). The result is displayed in 3D.

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2

4 5

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(e)

(b)

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(d)

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Fig. 2 Stages in the location (a)-(d) and extraction (e)-(i) process of the anterior cruciate ligament

2 Location of the Cruciate Ligament Structure on the T1W MR Series The T1W MR knee images, which were analysed, have size 256 × 256 pixels. The average length of the side of a rectangle enclosing the CL structure is equal about 80 pixels. In order to increase efficiency of computational procedures, it is very important to reduce the size to the region of interest (ROI 2D) including cruciate ligament structure. The proposed automatic method of location of the CL on the T1W MR knee images is based on fuzzy C-means (FCM) algorithm with median modification. Standard FCM algorithm is widely used in many clustering approaches. Its advantages include a conceptual and computational simplicity and the ability to model uncertainty within the data. FCM has also several weaknesses. It does not incorporate spatial context information which makes it sensitive to noise and image artifacts. In this paper a modified method of FCM is used for the clustering. The FCM objective function is modified by adding a second term, which formulates a spatial constraint based on the median estimator. Then, the final formula for FCM median modified can be expressed as K

J(U, V) =

N

∑ ∑ uknf r

  xn − vk 2 + α MedF(xn , Z) − vk 2 .

(1)

k=1 n=1

where MedF(xn , Z) = median(S), S = neighbourhood(xn , Z) and Z determines the size of the mask. The processed clinical T1W MR knee by the FCM median modified is shown in the Fig. 2b.

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On the basis of the analysis of each profile in every slice of the T1W MR knee after fuzzy clustering, a main axis (no.1 in the Fig. 2c) running along the thighbone and tibia is determined. The main axis is determined according to following formula " # th = max L pr (k) , f or each L pr (k) = 0, (2) k

where L pr (k) denotes number of nonzero values of the pixel intensity in the k profile. When several profiles meet condition (2), the profile of the lowest nonzero pixel value is chosen. In the next step edges of a ROI 2D containing the anterior and posterior cruciate ligaments are found according to following rules: • Upper edge (axis 4 in the Fig. 2c) " # max du u

(3)

where du - distance between main axis (no.1) and right edge of thighbone for u-profile, • Lower edge (axis 5 in the Fig. 2c) " # max d p (4) p

where d p - distance between main axis (no.1) and right edge of tibia for p-profile, • Right edge (axis 2 in the Fig. 2c) has been determined on the basis of the axis 1 shifted by (4). • Left edge (axis 3 in the Fig. 2c) has been determined on the basis of the axis 1 shifted by following formula: " # max d ple f t , (5) p

where d ple f t - distance between main axis (no.1) and left edge of tibia for pprofile. The region of interest ROI 2D including both ACL and PCL structures determined according to above rules is shown in the Fig. 2d.

3 Extraction of the Cruciate Ligament Structure from the T1W MR Series In order to increase the efficiency of computational procedures, ROI 2D including CL structure has been outlined. The next step of that process is an extraction of the cruciate ligament structure using the fuzzy connectedness approach. A generalized definition of fuzzy connectedness [5] is based on the fuzzy affinity relation and introduces an iterative method, that permits the fuzzy connectedness to be determined with respect to the chosen image pixel - seed point (the green point in Fig. 2e). This paper bases on a simplified graph-based view for Z 2 [2],

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that uses a digital topology approach. Let zi = (zi1 , zi2 ) denote an image pixel, and f (zi ) its signal intensity. Let all the image pixels zi constitute nodes of a graph. In the practical approach, within the graph, each pixel is interconnected with all its spatially adjacent pixels. The adjacency may be defined in terms of a fuzzy 2-ary relation, but usually an intuitive [2] hard relation of 9-, or 25-connectedness is used. Every direct zi -z j link in the graph has a strength assigned to it, that is equal to the value of a reflexive and symmetric fuzzy affinity relation for the two connected nodes μκν (zi , z j ). The fuzzy affinity relation models the similarity of adjacent pixels. Within the graph, for each two pixels zk , zl , a path consisting of zero or more links can be found. A set of all existing path from zk to zl is denoted as Pzk zl . To each path p from Pzk zl , the strength μN (p) is assigned as the strength of its weakest link, i.e. the lowest value of affinity for two constituting nodes ([0,1]). The fuzzy connectedness can be then defined as a fuzzy relation: ∀zk zl : μκ (zk , zl ) = max [μN (p)].

(6)

p∈Pzk zl

The object segmentation is possible by thresholding the fuzzy connectedness relation (FC-based labeling and object extraction) or by comparing the fuzzy connectedness determined with respect to the given segmentation seed points belonging to the object and background (relative FC approach) [3]. In both direct, and relative FC-based segmentation tasks, the fuzzy affinity μκν is used to model the notion of similarity of adjacent pixel within the extracted object. Usually [5] the membership function is employed, that depends on the signal level of compared pixels, the local signal gradient, and the properties of the extracted object (defined in terms of mean and standard deviation parameters): ⎧ if zk = zl ⎨1 μκ (zk , zl ) = ω · G1 (zk , zl ) + (1 − ω ) · G2(zk , zl ) if zk = zl and adjacent (7) ⎩ 0 otherwise where ω ∈ [0, 1], and G1 , G2 are selected from (8), (9), (10) or (11). 

1 g1 (zk , zl ) = exp (−1) · 2 2s1



f (zk ) + f (zl ) − m1 2

2  ,

(8)

  1 g2 (zk , zl ) = exp (−1) · 2 (| f (zk ) − f (zl )| − m2 )2 , 2s2

(9)

g3 (zk , zl ) = 1 − g1(zk , zl ),

(10)

g4 (zk , zl ) = 1 − g2(zk , zl ),

(11)

where function f (zk ) and f (zl ) denoting signal level of zk and zl [3]. In the first step of the fuzzy connectedness approach is requisited to choose image pixel - seed point. That point has to be included in the extracted anatomical

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(a)

(b)

Fig. 3 Extracted (a) ACL and (b) PCL structures superimposed over the original T1W MR series (Fig. 1)

structure - anterior or posterior cruciate ligament (Fig. 2e). In the next step the above described calculates are executed. The result of the fuzzy connectedness approach is shown in Fig. 2f, where we obtained unwanted structures besides the ACL structures. In order to remove unwanted structures the morphological operations: erosions, dilation and opening have been implemented. It breaks narrow links of ligament and unwanted structures. The latter are then removed (Fig. 2g). The result is superimposed over the original image (Fig. 2h,i). The extracted ACL structures are shown in Fig. 3a. The same methodology is applied to extract the posterior cruciate ligament (Fig. 3b) and bones of the knee joint (Fig. 5). These images allowed a 3D model of both PCL (Fig. 4) and knee bones (Fig. 6) to be built. This spatial structure is created through layer composition of the base images by using a linear interpolation.

4 Numerical Results and Conclusion The algorithm has been tested using MRI slices of the knee joint with both injured and normal anterior cruciate ligament. For all cases the segmentation process based on fuzzy connectedness has been repeated for each MR slice including the anterior and posterior cruciate ligament separately. The methodology has been tested on 24 (11 injured and 13 normal anterior cruciate ligament) clinical T1W MR knee studies. In 21 cases the proposed method location of the cruciate ligament on the T1W

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Fig. 4 3D visualization of the PCL structures obtained for T1W MR series (Fig. 1)

Fig. 5 Extracted bones of the knee joint from the original T1W MR series (Fig. 1)

MR knee images has been executed correctly. Errors connected with localization process have been caused by the following factors: a ligament is broken together with the thighbone, a lack of the location of thighbone and tibia along the same axis, and a location of the knee joint in the extreme part of the slice. In 19 cases the anterior cruciate ligament structure has been extracted correctly whereas posterior cruciate ligament has been extracted correctly in all cases. In two cases of serious injuries anterior cruciate ligament a modification of the methodology is required. The fuzzy connectedness procedure is completed by the fuzzy c-means function. On the basis of the described methodology a software application has been built. This application is dedicated for the knee joint diagnosis and it makes possible the registration process of the T1W and T2W MR series ([6], [7], [8]) and the three-dimensional visualization process of following structures: ACL, PCL (Fig. 4) and bones (Fig. 6) of the knee joint.

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Fig. 6 Bones’ 3D visualization obtained for T1W MR series (Fig. 1)

Application of the fuzzy connectedness and fuzzy c-means in the anterior and posterior cruciate ligament segmentation, and obtained results seem to be a very promising method in the three-dimensional visualization of that structures. Segmentation and three-dimensional visualization of the cruciate ligament is the initial stage in building a computer aided diagnosis of the knee joint, including the three-dimensional visualization and quantitative analysis.

References 1. Ciszkowska-Łyso´n, B.: Anatomia wie¸zadeł krzy˙zowych w badaniu rezonansu magnetycznego. Acta Clinica 4(1), 321–330 (2001) 2. Eckhardt, U., Latecki, L.J.: Topologies for the digital spaces Z 2 and Z 3 . Computer Vision and Image Understanding 90, 295–312 (2003) 3. Kawa, J., Pie¸tka, E.: Automated Fuzzy-Connectedness-Based Segmentation in Extraction of Multiple Sclerosis Lesions. In: Information Technologies in Biomedicine, ITIB 2008, pp. 149–156 (2008) 4. Pasierbi´nski, A., Jarza¸bek, A.: Biomechanika wie¸zadeł krzy˙zowych. Acta Clinica 4(1), 284–293 (2001) 5. Udupa, J.K., Samarasekera, S.: Fuzzy connectedness and object definition: Theory, algorithms, and applications in image segmentation. Graph. Models Image Processing 58, 246–261 (1996) 6. Zarychta, P.: Automatic Registration of the Medical Images - T1- and T2-weighted MR Knee Images. In: International Conference Mixed Design of Integrated Circuits and Systems, MIXDES 2006, pp. 741–745 (2006) 7. Zarychta, P.: Location and 3D visualization of the cruciate ligament in the MR knee images on the basis of fuzzy logic. PhD Thesis, Silesian University of Technology, Gliwice (2006) 8. Zarychta, P.: Posterior Cruciate Ligament - 3D Visualization. In: V International Conference on Computer Recognition Systems, CORES 2007, pp. 695–702 (2007)

Computerized Evaluation of Abnormal Hand Bone Patterns in Skeletal Dysplasias Arkadiusz Gertych, Morgan Clond, Ralph Lachman, and David Rimoin

Abstract. Assessment of bone disproportion is one of the routine radiological procedures frequently performed at a skeletal dysplasia diagnosis center. The existing knowledge on skeletal dysplasia patterns is more qualitative than quantitative, and the commonly applied diagnostic procedure is the manual, atlas-based evaluation of radiographs (including the hand) by an expert. A computer-aided diagnosis package (CAD) for bone age assessment was improved to analyze hand radiographs of skeletal dysplasia subjects with manifested hand bone abnormalities. The CAD software can automatically measure the lengths of phalangeal bones, compare them with those obtained from normal subjects collected in the Digital Hand Atlas (DHA), and recognize selected abnormality patterns. We have tested our method based on brachydactyly type A cases from the skeletal dysplasia diagnosis center that were matched with subjects from DHA in the age range of 2-12 years. New quantitative results obtained from this study have the potential to enrich the qualitative criteria currently utilized in the manual evaluation of abnormal bones, and thereby improve the performance of the diagnostic procedure. Arkadiusz Gertych Department of Surgery, Cedars-Sinai Medical Center, 8700 Beverly Blvd, Los Angeles, CA 90048 e-mail: [email protected] Morgan Clond Cedars-Sinai Graduate Program in Biomedical Science and Translational Medicine, 8700 Beverly Blvd, Los Angeles, CA 90048 e-mail: [email protected] Ralph Lachman International Skeletal Dysplasia Registry, Medical Genetics Institute, Cedars-Sinai Medical Center, 8700 Beverly Blvd. PACT 4, Los Angeles, CA 90048 David Rimoin Medical Genetics Institute, Cedars-Sinai Medical Center, 8700 Beverly Blvd. PACT 4, Los Angeles, CA 90048

E. Pi˛etka and J. Kawa (Eds.): Information Technologies in Biomedicine, AISC 69, pp. 123–132. c Springer-Verlag Berlin Heidelberg 2010 springerlink.com 

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1 Introduction Skeletal dysplasias (SDs) are uncommon diseases classified into more than 300 disorders of bone and cartilage growth resulting in abnormal shape and development of the skeletal system. In most cases, SDs are caused by a genetic mutation and are often detected in the newborn period or during infancy, however some disorders may not manifest until later in childhood. Conventional radiographic examination remains the most useful mean of studying the dysplastic skeleton. The diagnostic procedure is in general time consuming, complicated and requires an expert (a pediatric radiologist or medical geneticist) with long term experience who evaluates a series of radiographs of different parts of the skeleton, including the hand. To properly classify a case, the reading is often supported by dysplasia atlases and as part of the routine, the subject’s bone age is also assessed. Since the availability of experts capable of reading such radiographs is very limited, the examinations are often sent to referral centers to obtain the best possible diagnostic opinion (Fig.1). It is important to give the specific diagnosis in each case, so that an accurate prognosis can be given and proper genetic counseling provided [1]. The brachydactylies are a group of skeletal dysplasia disorders (classified into several patterns: A1, A2, A3, A4, B, C, D, and E) in which the affected individuals may have short stature and short or stubby fingers and toes [2, 3, 4, 5]. The type A brachydactylies have the shortening restricted mainly to the middle phalanges. Another anomaly is the development of a cone shape epiphysis with the apex protruding into the adjacent metaphysis. These epiphyses close prematurely, leading to short tubular bones. Such radiological findings result in abnormal bone age assessment during the diagnostic procedure. Although the radiological description of brachydactyly patterns and other SDs have been documented based on individually classified and published cases, the present scientific knowledge in this field is rather qualitative. There is still no sufficient quantitative evidence about the range of abnormalities affecting individual bones within the scope of a particular disorder or pattern, especially if compared with standards (normal hand bone patterns). Availability of such data will not only increase the knowledge in the relevant domains but can also constitute a valuable component in the current diagnostic workup of SDs. The capabilities of computerized evaluation of abnormal hand radiographs can be enriched by automatic classification of phalangeal bones which is suitable for the recognition of SD cases throughout the methodology we propose (Fig.1).

2 Materials The International Skeletal Dysplasia Registry (ISDR) at our institution has the largest collection in the world of cases and specimens dedicated for research, diagnosis, management and studies of etiology of the SDs [6]. From the collection of

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Fig. 1 A typical workflow in the diagnosis of a skeletal dysplasia case with a newly proposed component (dashed lines). Multiple radiographs of a subject’s skeleton and other supporting documentation are sent to the International Skeletal Dysplasia Registry for diagnosis and counseling. The diagnostic report is sent back to the ordering institution. The Digital Hand Atlas together with CAD can augment current qualitative knowledge by incorporating quantitatively described standard bone patterns.

125 cases of brachydactylies at ISDR, several hand X-rays of subjects with brachydactyly type A, including patient demographic data, were initially selected and digitized on a DICOM compliant scanner with 16bit/pixel gray scale resolution. Private patient information was anonymized. A group of reference hand radiographs of normally developed Caucasian subjects between 2-12 years of age was selected from the DHA [7, 8] to closely match and compare with the abnormal cases. An example of a hand image of a brachydactyly A subject with an age and sex matching radiograph of a normal subject is shown in Fig. 2.

3 Methods A CAD for bone age assessment has already been developed [9, 8]. The package includes: unsupervised procedures for localization, segmentation and feature extraction of ossification centers in distal and middle phalanges of IInd-IVth finger [10, 11, 12], radius and ulna bones [13], and an engine for automated bone age evaluation utilizing quantitative features extracted from ossification centers [14, 8]. In order to test the usefulness of this CAD in quantitative characterization of selected types of brachydactylies, some new capabilities including: a) localization and tracing of axes through Ist (thumb) and Vth finger, b) length measurement of the middle phalangeal bones in II-Vth finger, and c) length measurement of the proximal bone

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(a)

(b)

Fig. 2 Example hand radiographs of 12 year old female Caucasian subjects: a) brachydactyly type A4 from ISDR, and b) normal matching subject from DHA

of the Ist finger were supplemented to our CAD package. Although several other papers have been dedicated to hand radiograph analysis [15, 16, 17] the parameters measured through b) and c) have not been reported so far. For the localization and tracing of the Vth finger axis we extended the approach described in [11] which has been successfully applied to the detection of II, III and IVth finger. Middle phalanges of IInd-Vth finger can be directly measured utilizing points of interest found during routine analysis of distal and middle phalanx growth plate regions [10, 14] that are mapped back onto the original image Fig. 3a In order to locate the proximal bone of the thumb a new procedure is proposed. The binary hand image is first scanned row-wise from the right side Fig. 3b A minimal distance between right border of the image and the hand object marks the thumb’s tip pthb . Row-wise scanning continues from the tip downward along the left and right sides of the thumb’s contour. The scanning procedure is interrupted if two points are reached: pra - the upper border of the radius and ulna region on the right side, and pII - the contour of the IInd finger on the left side, respectively. Next, the thumb thickness tthb is approximated as a horizontal distance between points of its contour at the level of pII . Then a profile is traced, starting from pthb until the level of pra is reached. The position of the profile is controlled by two factors: the contour of thumb recorded during scanning and its distance from the right side border of the image, slightly varying along the profile according to tthb value. Finally, the profile is analyzed using the method presented in [11] to isolate and measure the proximal bone of thumb. In the last step, lengths of middle phalanges of IInd-Vth finger and Ist finger proximal bone are automatically collected in this way.

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Hand radiographs of brachdactyly A1-A4 subjects selected from ISDR and radiographs of normal subjects from DHA were analyzed by our modified CAD. Next individual measurements were normalized (expressed as ratios) and compared to respective ratios from group of age and sex matched normal subjects. Furthermore to prove feasibility of the study we implemented a rule-based strategy utilizing normalized measurements (ratios) of IInd-Vth middle phalanges and length of proximal bone of thumb to detect brachydactyly type A1-A4 abnormality. The evaluation is based on a logical decision tree implemented in the CAD software (Fig. 4).

(a)

(b)

Fig. 3 New processing steps implemented into the CAD: a) measurements of middle phlanageal bones, and b) a strategy of tracing a profile through the Ist finger

4 Results A new module offering automated and quantitative analysis of middle phalanges in hand radiographs was implemented into our CAD software (Fig.5). Bone measurements from the reference DHA data (Caucasian subjects) were performed first. Mean values and standard deviations were calculated to define ranges of normal bone deviation within all age groups for males and females. Next, measurements from abnormal radiographs were extracted, and mapped onto the data from normal subjects to validate the rule-based evaluation of brachydactyly type A patterns (Fig.6 and Fig.7) . The results are included in Tables 1 and 2, respectively. In the case of a 12 year old female with brachydactyly type A4, the ratio of IIndmiddle /IIIrdmiddle is located 6.25 standard deviations outside of the range of matching normals. The

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Fig. 4 Rule-based strategy in the automated evaluation of barachydactyly type A (A1, A2, A3 and A4) patterns implemented on the CAD platform

2 year old male case is solved in the first level of the decision tree (Fig. 4) due to the missing middle phalanx of the Vth finger. Furthermore, the length ratio between IIndmiddle /IIIrdmiddle deviates from the mean value in the normal group of subjects by 5.63 standard deviations. The third case (4 year old male) is less straightforward because the formation of the skeleton is delayed compared to normal radiographs in the 4 year old age group. Moreover, the ratios of IIndmiddle /IIIrdmiddle and Vthmiddle /IVthmiddle are within the distance of 9 and 4 standard deviations from the mean values in the respective categories of normal ratios. The last two cases represent the brachydactyly A1 pattern. The software’s graphical user interface displays the image being analyzed with superimposed radiological findings and the regions of interest that are automatically extracted. Numerical results CAD automated assessments are exported to a file.

5 Conclusions This study is the first of its kind to combine quantitative statistical information, use of automated hand feature detection software, and real world radiographs for the quantitative diagnosis of skeletal dysplasias. For the purpose of proving the concept of computerized evaluation of bone abnormalities, we implemented automated

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Fig. 5 CAD window with superimposed phalangeal regions and Ist-Vth finger axes and radius and ulna region

Fig. 6 Examples of normal phalange growth in male Caucasian subjects

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Fig. 7 Examples of finger length ratios maintained throughout development of male Caucasian subjects Table 1 Ranges of proximal and middle bone measurements (mean ± std) obtained in three age groups of normal subjects matched to our case study subjects Age, sex 12y Female 2y Male 4y Female

Ist proximal mm 23.9 ± 2.0 13.5 ± 1.0 15.5 ± 1.0

IIndmiddle mm 18.5 ± 2.2 10.0 ± 1.0 11.5 ± 0.4

IIIrdmiddle mm

IVthmiddle mm

23.0 ± 2.4 12.6 ± 0.8 14.8 ± 0.9

21.8 ± 2.2 12.2 ± 1.0 14.3 ± 1.0

Vthmiddle mm 14.9 ± 2.1 8.47 ± 1.0 9.22 ± 1.1

Table 2 Comparison of measurement ratios of abnormal bones (type of brachydactyly pattern) vs. ranges in matching groups of normal subjects from Table 1 Ratio Age, sex 12y Female 2y Male 4y Female

IIndmiddle /IIIrdmiddle abnormal (pattern) normal 0.55 (A4) 0.35 (A1) 1.04 (A1)

0.8 ± 0.04 0.8 ± 0.08 0.77 ± 0.03

Vthmiddle /IVthmiddle abnormal (pattern) normal 0.48 (A4) 0.00 (A1) 0.80 (A1)

0.68 ± 0.05 0.69 ± 0.03 0.64 ± 0.04

quantification of brachydactyly type A and its four major subtypes. Our CAD can automatically perform hand radiograph evaluation in selected SD cases via extraction of new quantitative features that can be considered in the diagnosis making process. We also established a framework to further enhance the diagnostic capabilities of CAD to work with a larger data collection from the ISDR center.

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Our study elucidates some key points and potentials for the future of CAD in assessing skeletal pathologies. The measurements extracted from phalanges may be used in the detection of certain SDs, but first of all they provide a quantitative reference which can augment and improve the current clinical standard in the diagnostic workup at a skeletal dysplasia registry center. Besides the large variety of SDs, the possible combinations of their manifesting features is on a level of complexity that makes them extremely time consuming to diagnose using the standard approach, which is using the reference books and atlases. On the other hand these tasks can be facilitated by software-based solutions automatically performing measurements, utilizing databases and classifiers to arrive at quantitated hand radiograph analysis. In addition, improved speed and objectivity can also be achieved through CAD. Although our approach was successfully applied to the analysis of a small set of cases, we also conclude that the automated analysis of the image data from patients with manifested skeletal abnormalities is very challenging. The difficulties lie in the large tolerance of the radiograph acquisition parameters among institutions. This mainly includes acquisition techniques (film-based or computed radiography), different exposure settings resulting in significant contrast discrepancy in the analyzed images. A nonstandard hand placement on the image poses additional difficulties. To this end, the implementation of digital radiography will become essential in the radiograph standardization process. It is clear that continued input and support from radiologists and medical geneticists will be essential to improving accuracy of this CAD software and the range of computer detectable dysplasias. The widespread use of CAD could ultimately contribute to identification and more specific quantitative classification of skeletal abnormalities, and the automated accrual of epidemiological information to ultimately increase the knowledge in relevant fields. Acknowledgements. This work was supported in part by an NIH Program Project Grant HD22657 and a grant from the Department of Surgery at Cedars-Sinai Medical Center.

References 1. Rimoin, D.L., Lachman, R.S.: Genetic disorders of the osseous skeleton. In: Beighton, P. (ed.) McKusick’s Heritable disorders of connective tissue, ch. 14, 5th edn. (1992) 2. Spranger, J.W., Brill, P.W., Poznanski, A.K.: Bone Dysplasias, 2nd edn. Oxford University Press Inc., New York (2002) 3. Fitch, N.: Classification and identification of inherited brachydactylies. Journal of Med. Genet. 16(1), 36–44 (1979) 4. Temtamy, S.A.: Classification of hand malformations as isolated defects: an overview. J. Genet. Hum. 30(4), 281–290 (1982) 5. Lachman, R.: Taybi and Lachman’s Radiology of Syndromes. Metabolic Disorders and Skeletal Dysplasias, 5th edn., Mosby Philadelphia (2006) 6. Rimoin, D.L., Cohn, D., Wilcox, W., Krakow, D., Lachman, R.: The International Skeletal Dysplasia Registry. In: 6th International Skeletal Dysplasia Society Meeting, Warrenton, VA (2003)

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7. Cao, F., Huang, H.K., Pietka, E., Gilsanz, V.: Digital hand atlas for web-based bone age assessment: system design and implementation. Comput. Med. Imag. Grap. 24, 297–307 (2000) 8. Gertych, A., Zhang, A., Sayre, J., Pospiech-Kurkowska, S., Huang, H.K.: Bone age assessment of children using a digital hand atlas. Comput. Med. Imag. Grap. 31(4-5), 322–331 (2007) 9. Pietka, E., Pospiech, S., Gertych, A., Cao, F., Huang, H.K., Gilsanz, V.: Computer automated approach to the extraction of epiphyseal regions in hand radiographs. J. Digit. Imaging 4(4), 165–172 (2001) 10. Pietka, E., Gertych, A., Pospiech, S., Cao, F., Huang, H.K., Gilsanz, V.: Computer assisted bone age assessment: image processing and epiphyseal/metaphyseal ROI extraction. IEEE T Med. Imaging 20, 715–729 (2001) 11. Pietka, E., Pospiech, S., Gertych, A., Cao, F., Huang, H.K., Gilsanz, V.: Computer automated approach to the extraction of epiphyseal regions in hand radiographs. J. Digit. Imaging 14(4), 165–172 (2004) 12. Gertych, A., Pietka, E., Liu, B.J.: Segmentation of regions of interest and post segmentation edge location improvement in computer aided bone age assessment. Pattern Anal. Appl. 10(2), 115–123 (2007) 13. Tsao, S., Gertych, A., Zhang, A., Liu, B.J., Huang, H.K.: Automated bone age assessment of older children using the radius. In: Andriole, K.P., Siddiqui, K.M. (eds.) Proceedings of the SPIE Medical Imaging 2008: PACS and Imaging Informatics, vol. 6919, pp. 69190E–69190E-9 (2008) 14. Pietka, E., Pospiech-Kurkowska, S., Gertych, A., Cao, F.: Integration of computer assisted bone age assessment with clinical PACS. Comput. Med. Imag. Grap. 27(2-3), 217–228 (2003) 15. Hsieh, C.-W., Jong, T.-L., Tiu, C.-M.: Bone age estimation based on phalanx information with fuzzy constrain of carpals. Med. Bio. Eng. Comput. 45, 283–295 (2007) 16. De Luis-Garcia, R., Martin-Fernandez, M., Arribas, J., Alberola-Lopez, C.: A fully automatic algorithm for contour detection of bones in hand radiographs using active contours. In: Proceedings of the IEEE International Conference on Image Processing (ICIP 2003), vol. 3, pp. 421–424 (2003) 17. Tiu, C.-M., Liu, T.-C., Hsieh, C.-W., Niu, D.-M., Chen, J.-D., Jong, T.-L.: Turner syndrome phalangeal screening based on a two-stage linear regression concept. Pediatr. Int. 4(51), 453–459 (2009)

Method of Brain Structure Extraction for CT-Based Stroke Detection Aleksandra Rutczy´nska, Artur Przelaskowski, Magdalena Jasionowska, and Grzegorz Ostrek

Abstract. A fully automated method for extracting brain structures from computed tomography images by employing adaptive filtering and finite Gaussian Mixture Modeling (GMM) with context-based enhancement is proposed. Generally, the method is composed of two phases. First, adaptive partial mean filter for noise removal and edge sharpening is used. The second phase is the multistage segmentation. Initial segmentation step concerning brain extraction from skull and non-brain tissue defines a region of interest (ROI) for further processing. Each pixel in ROI is assigned to one of three semantically fundamental classes - white matter (WM), gray matter (GM) and cerebrospinal fluid (CBF) and two extended classes of specific tissue. GMM with expectation-maximization algorithm (EM) is employed to assign initial class labels to image pixels and followed by context information modeling through Contextual Bayesian Relaxation Labeling (CBRL). The CBRL algorithm incorporates local neighborhood information and iteratively refines the outcome of GMM classification. The results of proposed approach have been verified by extracting susceptible-to-stroke regions (SSR) processed for hypodensity distribution estimation. The extracted structures are more smooth and reliable in comparison to region growing segmentation results.

1 Introduction Stroke is the third leading cause of death and leading cause of disability in developing countries [1]. However, ischemic stroke imaging with instant visualization of acute symptoms is still a challenging problem. Computed tomography (CT) is Aleksandra Rutczy´nska · Artur Przelaskowski · Magdalena Jasionowska · Grzegorz Ostrek Institute of Radioelectronics, Warsaw University of Technology, Nowowiejska 15/19, 00-665 Warszawa, Poland e-mail: {arachock,artur,mjasiono,gostrek}@ire.pw.edu.pl E. Pi˛etka and J. Kawa (Eds.): Information Technologies in Biomedicine, AISC 69, pp. 133–144. c Springer-Verlag Berlin Heidelberg 2010 springerlink.com 

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a method of choice in stroke imaging. Some advantages of CT over magnetic resonance imaging (MRI) can be pointed. Amongst them, the following facts opt for CT: widespread availability (CT devices outnumber MRI equipment), short imaging times (vital with unconscious patients) and fewer limitations, e.g. CT is irreplaceable in case of patients with implanted biomedical devices (such as cardiac pacemakers) or ferromagnetic materials. CT helps to distinguish ischemic from hemorrhagic stroke or other brain diseases. Unfortunately, early signs of ischemic stroke in acute phase (up to 6 hours from onset), which are extremely useful for successful thrombolytic treatment, are hardly visible on CT scans. This was a motivation for the development of computed-aided diagnostics in the field of stroke imaging [2, 3, 4, 5]. An important role of susceptible-to-stoke region (SSR) extraction was proven in earlier research on stroke imaging. A tool for computer assisted support of acute stroke diagnostics was developed. The software used data hypodensity mapping and would be referred to as Stroke Monitor (SM) [6]. Proper segmentation of brain structures, especially delimitation of CBF structures (brain ventricles and cerebral sulci), played crucial role in reducing false indications of SM method. SSR extraction was based on region growing segmentation with adaptively selected thresholds. In some cases, segmented CBF structures were rough, ill-defined, spread out or too compact. Optimization of SSR segmentation was the general purpose of our research. First of all, SSR segmentation as a first step of hypodensity map estimation has to be more accurate, flexible and reliable for all test cases. Unlike research on brain segmentation from MRI data, CT literature is very scarce. In [7] comparison of manual and semiautomatic methods with thresholding was performed. Region-based methods in [8] were used to brain structures segmentation in MRI. Fuzzy C-means (FCM) algorithm was used in [9] and [10] for brain hemorrhagic analysis. In [11] modified FCM was proposed, it incorporates context information. Segmentation using Bayesian classifier in CT is proposed in [12]. In this paper we proposed the method for white/gray matter and CBF structure segmentation. In the preprocessing stage adaptive filtration is used to denoise the image and enhance structures. Motivation to use implementation of Adaptive Partial Averaging Filter (APAF) [5, 13] was generally low signal to noise ratio (SNR) of CT scans, possible presence of artifacts and unclear structure delimitation in source data. Next, deskulling the brain tissue based on adaptive algorithm of 3D region growing was determined. Fundamental stage of SSR segmentation was based on stochastic image modeling. Incorporating context information revealed high potential of designed method. Input image is subject to tissue-of-interests extraction method based on sequence of selected concepts implemented and adjusted to perform efficient stroke detection. Experimental verification of the method were concluded.

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2 Method Stochastic image modeling is defined as a partitioning of the image into distinctive meaningful regions based on the statistical properties of global and local gray-level pixel dependencies. Suitable model selection depends on the pixel value distribution and characteristics of pixel contexts, i.e.: a) regional data distributions related to image data distribution, b) statistical characteristics of the nearest pixel neighborhood associated with different regions. Such components of image model are possibly justified in terms of imaging physics, acquisition limitations, visualized object properties, etc. Context data dependencies correctly redefine the membership of the pixel to each of the regions present in the image [14]. We assumed that each pixel belongs to one of three fundamental classes: cerebrospinal fluid (CBF), white matter (WM) and gray matter (GM) and two additional classes of deep hypodensity and bone artifacts. Pixel image refers to gray level distribution associated with finite Gaussian Mixture Model (GMM) used for image analysis. Moreover, contextual Bayesian relaxation model incorporates statistical properties of pixel neighborhood. Fig.1 shows flow chart of the proposed method.

Fig. 1 Flow chart of proposed method of susceptible-to-stoke region extraction for CT-based stroke detection

Firstly, noise1 removal operation was performed on a original CT data. Implemented APAF method outlined structure contours and enhanced subtle regional distinctions, additionally. Then brain region was determined – bones and non-brain tissue were excluded from the images. Key stage of the method, i.d. initial SSR extraction, was based on GMM region segmentation with the parameters selected 1

Approximately of 4 Hounsfield Units [HU].

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according to a priori analysis of stroke detection requirements and optimized with maximum likelihood estimation by expectation-maximization (EM) algorithm. To simplify the calculations initial regions were estimated based on the assumption that all pixels are independent. In further steps, in order to make the segmentation more reliable and accurate, segmentation refinement was performed based on CBRL algorithm [15], which incorporates local neighborhood information. The assumptions and fundamental rules implemented in the key stage of presented SSR extraction method were shortly discussed in the following subsections.

2.1 Stochastic Image Modeling Relationships between neighboring pixels are well described by Bayesian conditional probabilities of m-order Markov model with memory (i.e. conditional source model). However, classification rules based on conditional data dependencies of higher order models are overly complicated, number of probabilities increases exponentially for enlarged context resulting in a problem of limited statistical reliability of the model (i.e. context dilution). To simplify image model and make it computationally acceptable, finite mixture model of regions was used with assumption that the whole image can be approximated by an independent and identically distributed random field. Local data dependencies were complied as follows: GMM was initialized by grouping-classification procedure of k-means and k-nearest neighbor classifier and followed by complementary context image modeling taking into consideration labels assigned to the pixels in the nearest neighborhood. More precisely, we assume that image contains K regions (classes) and pixel labels are random variables. Thus, a whole image of N pixels can be modeled by independent and identically distributed (iid) random field X, given the joint probability density function: N

K

P(x) = ∏ ∑ πk Pk (xi )

(1)

i=1 k=1

where x = [x1 , . . . , xN ] and x ∈ X, πk is a weighting factor and Pk (xi ) is conditional region probability density function (pdf) of k class (region), i.e. Pk (xi ) = P(xi /Rk ). Given image is a concrete realization of X. Considering statistical image properties, generalized Gaussian pdf was used: Pk (xi ) =

  αβk 1 Γ (3/α ) 1/2 exp[− | βk (xi − μk ) |α ], α > 0, βk = 2Γ (1/α ) σk Γ (1/α )

(2)

where μk is the mean, σk is the standard deviation, Γ (·) is the gamma function and α defines distribution shape.

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Because of physical conditions and statistical estimates of CT scan data, we assumed α = 2, i.e. Gaussian pdf with two parameters μk and σk , for all regions. Therefore, we have   1 (xi − μk )2 2 Pk (xi | μk , σk ) = √ exp − (3) 2σk2 2πσk Moreover, other global parameter K was set to 5 based on stroke detection requirements and experimental verification. Because of precise CBF structure segmentation, we decided to define two classes of hypodensity: weak and deep. Subsequently, two classes of white and grey matter were extended by additional class of marginal tissue distorted by bone artifacts. Next, image model was optimized by effective estimation of regional parameters of distributions, i.e. πk , μk and σk . Finally, pixels were labeled and image regions were determined according to Bayesian classification rule based on fixed local parameters and regional memberships of the image pixels. 2.1.1

Expectation – Maximization Algorithm

The objective of model identification (parameter estimation) is maximizing likelihood function or minimizing relative entropy between image histogram PF ( f ) and estimated pdf PX ( f ) of the image model P(x), where f is a gray level of source alphabet. To perform maximum likelihood estimation we used the most popular approach - expectation-maximization algorithm (EM). The EM first calculates Bayesian posterior probabilities and obtains parameter estimates (E step), then updates these estimates using mean ergodic theorem (M step). The successive iterations of the E and M steps increase the likelihood of the model parameters. Used criterion is minimization of relative entropy expressed by Kullback-Leibler distance: H(PF ||PX ) = ∑ PF ( f ) log f

PF ( f ) PX ( f )

(4)

The EM algorithm proceeds as follows 1. assumed global parameters are K = 5, α = 2 (0) (0) (0) 2. m = 0 iteration with parameter set g(0) = {πk , μk , σk , k = 1, . . . , K}, according to initial k-nearest neighbor classification 3. E step: for i = 1, . . . , N, k = 1, . . . , K count probabilistic membership (m)

(m)

zik =

πk Pk (xi ) (m)

∑Kk=1 πk Pk (xi )

4. M step: for k = 1, . . . , K update parameter estimates

(5)

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⎧ (m+1) (m) ⎪ = N1 ∑Ni=1 zik ⎪ πk ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ (m+1) (m) 1 μk = (m+1) ∑Ni=1 zik xi N πk ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ 2(m+1) (m) (m+1) 2 1 ⎪ ⎩σ = ) ∑N z (xi − μ k

(m+1)

N πk

i=1 ik

(6)

k

5. When condition |H (m) (PF ||PX ) − H (m+1) (PF ||PX )| > ε is satisfied increment m = m + 1 and go to E step; otherwise save optimal g. We used GMM-EM implementation from PRTools 4 [16] with slight modification to make it more flexible. 2.1.2

Bayesian Classifier

Classification problem consists of prediction of the pixel label k ∈ K (i.e. to predict its membership to one of the image classes) based on feature vector x. The classifier d : x → K with accurate prediction needs to be found. Bayes theorem is a conditional probability of event A given event B. Bayes classifier is based on a Bayes rule P(A | B) =

P(B | A)P(A) P(B)

(7)

Bayes rule is used to determine posterior probabilities for pixel to be a member of each of the classes present in the image. The rule for each pixel indexed i, i = 1, . . . N classified to class k, k = 1, . . . K is given by P(k | xi ) =

πk Pk (xi ) K ∑ j=1 π j Pj (xi )

(8)

where P(k | xi ) is a posteriori probability (also referred to as regression function) that pixel belongs to class k given xi ; πk – a priori probability that pixel belongs to class k (class frequency) with assumption ∑Ki=1 πi = 1; Pk (xi ) – pdf of the feature vector x in k-th class. Bayesian classifier form of pixel labeling is as follows dB (xi ) = arg max P(k | xi ) = arg max πk Pk (xi ) k

k

(9)

where P(k | xi ) is given in equation 8. 2.1.3

Context Modeling

In GMM we assumed that pixels in the image are independent to simplify calculations. To refine estimated regions and to make them more accurate, context information should be included in the model. Modified CBRL method incorporating local neighborhood information was used as compliment of GMM model.

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Let ςi be a neighborhood of the i-th pixel while m × m defines size of this neighborhood. Factor πk is estimated locally for each pixel as

πki = p(li | lςi ) =

1 m2 − 1

∑

I(k, l j )

(10)

j∈ςi , j=i

where li denotes label of pixel i and lςi is labels set of its neighbors, I stands for indicator function

1 if l j = k I(k, l j ) = 0 otherwise Algorithm CBRL can be summarized as follows 1. Iteration m = 0 with GMM-EM based pixel classification l(0) 2. Update pixel labels • Randomly order all image pixels for i = 1, . . . , N • Visit successive pixel according to random selection and update its label as follows (m) i(m) l j = arg{max πk Pk (xi )} (11) k

complied with

i(m) πk

modification according to equation 10.

3. If less than 1% pixels changed its label algorithm stops; otherwise increment m = m + 1 and go to step 2. Final SSR extraction is binarization of region map with two hypodensity classes included into non-SSR class and the rest segmented regions classified as SSR.

3 Results Presented method of brain structure extraction was optimized and verified on a set of 21 scans of selected test CT examinations. Chosen set consisted of difficult to segment cases indicated and analyzed by radiologist. Marked regions, especially CBF structures, were gold standard for efficiency assessment. Test set contained 265 CBF structures to be segmented correctly for stroke detection application. Two statistical measures - sensitivity and number of false positives per scan were calculated to assess the reliability and accuracy of the segmentation. We reached the sensitivity of 97% with 0.3 false positives per scan. Lower sensitivity was a result of omitting small, subtle sulci close to bone order which were misclassified as a white matter. False positives occurred in brain top scans for middle brain line. The detailed results of segmentation procedures were presented in the following figures. Results of APAF filtering in a context of less sophisticated methods were shown in Fig. 2. APAF performs better comparing to other filtration methods in terms of high noise reduction rate with simultaneous edge preserving as well as structures extraction.

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Fig. 2 CT scan filtering effects: source image (top left) is confronted with average filtering (top right), median filtering (all of which use kernel size 5x5) and APAF filtering

In the next figure (Fig. 3) the positive role of APAF filtration in CT image segmentation is presented. Segmentation performed on the non-enhanced CT data (without any filtration) depicts regions disturbed by the noise and significantly deviates from our expectations. Incorporating APAF-based processing results in segmentation that is coherent with the anatomy of imaged brain.

Fig. 3 The segmentation results influenced by APAF: source CT scan, effects of segmentation without APAF and the segmentation based on APAF-based image enhancement, respectively

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Results of segmentation of the regions non susceptible to stroke (i.e. CBF class) are compared with reference image (Fig. 4). Gold standard image was prepared by a radiologist who selected brain structures, which should be excluded from image as they can produce false positives indications in stroke detection procedure. Binarized image is the final result of SSR extraction for that case.

Fig. 4 Segmentation results for exemplar CT scan: reference image with marked regions, effects of 5 class segmentation and binarization for SSR extraction, respectively

An example of comprehensive 5 class segmentation output was presented in Fig. 5 and in Fig. 6. Selected scans of CT examination reflects diversity of achieved results for analyzed data set. On the last figure (Fig. 7) follow-up CT with visible stroke is confronted with classified image. Segmentation of the stroke area from the follow-ups could be beneficial in stroke size assessment for estimated pathology progression and therapy planning.

4 Conclusions Our method exhibits satisfactory results. Main advantage of the proposed algorithm is the fact that it has flexible parameter of the class numbers which could be adjusted to application requirements. Moreover, binarization procedure is susceptible to semantic image characteristics and a priori knowledge models (ontology). General method scheme was not fitted only to a specific CT data. It gives good results by employing statistical nature of the images. In future research we would further explore the efficiency level which is now degraded mainly by the artifacts (beam hardening artifacts). Better brain segmentation (ROI defining) method should be researched to remove the fifth class, which is now reserved for the artifacts from the bones. Context information in the third dimension should also be included.

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Fig. 5 Exemplar test CT data of successive source scans

Fig. 6 The effect of segmentation of CT scans presented in Fig. 5

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Fig. 7 Stroke area assessment for follow-up CT scan: source image and effects of proposed segmentation procedure, respectively

References 1. Chalea, J.A., Merino, J.G., Warach, S.: Update on stroke. Current Opinion in Neurology 17, 447–451 (2004) 2. Bendszus, M., Urbach, H., Meyer, B., et al.: Improved CT diagnosis of acute middle cerebral artery territory infarcts with density difference analysis. Neuroradiology 39(2), 127–131 (1997) 3. Maldjian, J.A., Chalela, J., et al.: Automated CT segmentation and analysis for acute middle cerebral artery stroke. AJNR Am. J. Neuroradiol. 22, 1050–1055 (2001) 4. Grimm, C., Hochmuth, A., Huppertz, H.J.: Voxel-based CT analysis for improved detection of early CT signs in cerebral infarction. Eur. Radiol., ECR European Congress of Radiology, B315 (2005) 5. Lee, Y., Takahashi, N., Tsai, D.-Y., Ishii, K.: Adaptive partial median filter for early CT signs of acute cerebral infarction. Int. J. CARS 2, 105–115 (2007) 6. Przelaskowski, A., Bargiel, P., Sklinda, K., Zwierzynska, E.: Ischemic Stroke Modeling: Multiscale Extraction of Hypodense Signs. In: An, A., Stefanowski, J., Ramanna, S., Butz, C.J., Pedrycz, W., Wang, G. (eds.) RSFDGrC 2007. LNCS (LNAI), vol. 4482, pp. 171–181. Springer, Heidelberg (2007) 7. Joe, B.N., Fukui, M.B., Meltzer, C.C., Huang, Q -s., Day, R.S., Greer, P.J., Bozik, M.E.: Brain Tumor Volume Measurement: Comparison of Manual and Semiautomated Methods. Radiology (1999) 8. Xuan, J., Adali, T., Wang, Y.: Segmentation of magnetic resonance brain image: integrating region growing and edge detection. In: Proc. International Conference on Image Processing, vol. C (1995) 9. Cheng, D.C., Cheng, K.-s.: Multiresolution based fuzzy c-means clustering for brain hemorrhage analysis. In: International Conference on Bioelectromagnetism 10. Loncaric, S., Cosic, D., Dhawan, A.P.: Hierarchical segmentation of ct head images. In: 18th Annual Conference of the IEEE Engineering in Medicine and Biology Society (1996)

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11. Mohamed, N.A., Ahmed, M.N., Farag, A.: Modified fuzzy c-mean in medical image segmentation. In: IEEE International Conference on Acoustics, Speech, and Signal Processing (1999) 12. Lauric, A., Frisken, S.: Soft segmentation of CT brain data. Tufts University 13. Takahashi, N., Lee, Y., Tsai, D.-Y., Ishii, K.: Novel noise reduction filter for improving visibility of early computed tomography signs of hyperacute stroke: evaluation of the filter’s performance-preliminary clinical experience cerebral infarction. Radiat. Med. 25, 247–254 (2007) 14. Tulay, A., Wang, Y.: Image Analysis and Graphics for multimedia presentation, ch. 8 15. Hummel, R.A., Zucker, S.W.: On the foundations of relaxation labeling processes. IEEE Trans. Pattern Anal. Machine Intell. 5(3) (1983) 16. Duin, R.P., Juszczak, P., Paclik, P., Pekalska, E., de Ridder, D., Tax, D.M.J., Verzakov, S.: PRTools 4 - A MATLAB Toolbox for Pattern Recognition. Version 4.1, Delft University of Technology (2007)

Combined DICOM and HL7 Viewer in Support of a Bridge from Content-Based Image Retrieval to Computer-Aided Diagnosis Petra Welter, Fatih Topal, Sebastian Jansen, Thomas M. Deserno, Jörg Riesmeier, Christoph Grouls, and Rolf W. Günther

Abstract. Content-Based Image Retrieval (CBIR) is a field of rising interest for the application in Computer-Aided Diagnosis (CADx). Exploiting the visual information hidden in the images for retrieval, it facilitates the identification of similar past examinations, thereby providing a second opinion. Still, CBIR is not an integral part of a radiologist’s daily work. A comprehensive representation of CBIR results in a standard format utilizing established clinical infrastructure together with all referenced comparable examinations will support a bridge from CBIR to CADx. In this paper, we introduce the general IRMACON viewer, a system that represents results from CBIR systems encoded as a DICOM Structured Reporting document in a layout adjusted for CADx. IRMACON also allows the insight into identified similar examinations for convenient comparison by accessing patient’s information and diagnostic findings from the Hospital Information System (HIS) using HL7 messages. Our system is embedded into the clinical setting and the radiologist’s workflow. We applied the IRMACON viewer to the Image Retrieval in Medical Applications (IRMA) framework.

1 Introduction Content-Based Image Retrieval (CBIR) [1] relates to the identification of images from a database using the visual information hidden in the images instead of attached textual annotations. Computer-Aided Diagnosis (CADx) can generally be defined as “a diagnosis made by a radiologist who uses the output of a Petra Welter · Fatih Topal · Sebastian Jansen · Thomas M. Deserno Department of Medical Informatics, RWTH Aachen University, Aachen, Germany e-mail: [email protected] Jörg Riesmeier ICSMED AG, Oldenburg, Germany Christoph Grouls · Rolf W. Günther Department of Diagnostic Radiology, RWTH Aachen University Hospital, Aachen, Germany E. Pi˛etka and J. Kawa (Eds.): Information Technologies in Biomedicine, AISC 69, pp. 145–152. c Springer-Verlag Berlin Heidelberg 2010 springerlink.com 

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computerized scheme for automated image analysis as a diagnostic aid” [2]. Physicians usually refer in their decision making of a diagnose to already closed cases with verified diagnostic results. In the context of CADx, the typical application of CBIR supports differential diagnosis, i.e. the distinguishing between two or more diseases by systematical comparison. The aim of CBIR is to provide the radiologist with a diagnostic aid by automatically identifying relevant past cases along with their diagnosis and other suitable information. This provides the radiologist with a second opinion, thereby enhancing the diagnostic assessment. CBIR has a high potential of improving the quality and efficiency of clinical care processes [3] and entails proved high benefits for CADx [4, 5, 6]. There are promising CBIR based CADx systems, the majority concentrating on a particular application area, e.g., lung cancer [7], mammography [8], computed tomographic images of the chest [9]. However, CBIR is not established yet in clinical routine. CAD schemes using CBIR approaches face a number of challenges and this technology needs more research work [10]. One essential factor is the seamless and robust integration into Picture Archiving and Communication Systems (PACS) and the radiologist’s workflow. This includes a comprehensive and integrative representation of the CBIR results along with all corresponding evidences adapted to the physicians needs. The appropriate and contextualized preparation of necessary data required for differential diagnosis delivers an indispensable brick in the bridge from CBIR to real CADx. A substantial requirement is the use of open standards and the integration with a hospital-wide communication structure [4]. Digital Imaging and Communications in Medicine (DICOM) Structured Reporting (SR) [11, 12] is an approved standard format for exchanging CADx results in clinical environments, e.g., for mammography [13, 14], which can be stored to and retrieved from PACS. Because of the many advantages [15, 12], the Integrating the Healthcare Enterprise (IHE) employs DICOM SR in several integration profiles [16]. There are several proposals for the general integration of CAD or CBIR systems into clinical environments, also based on DICOM SR documents, e.g., [17, 18]. That motivated us to apply DICOM SR encoded CBIR results in our concept presented in this paper. There are viewers capable of interpreting SR documents and producing a generic layout, but they are not adjusted to the special needs of CBIR for CADx. Diagnostic findings from different clinical departments, e.g. pathology, laboratory or endoscopy, are usually archived centrally by the Hospital Information System (HIS), utilizing the Health Level Seven (HL7) [19] protocol. Clinical viewers for diagnostic findings are usually not capable of integrating CBIR results or even CADx results in general. We close this gap and present in this paper the novel IRMACON viewer, a combined viewer for CBIR SR documents together with referenced diagnostic findings from HIS.

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2 Materials and Methods We first analyzed the general CBIR-based CAD scheme, in which we embedded our IRMACON viewer. Our proposed IRMACON viewer system makes use of DICOM SR and HL7. Relevant information on both is explained in the following. Thereafter, we analyzed requirements concerning a successful data capturing.

2.1 CBIR-Based CADx Scheme CADx systems with CBIR approaches incorporate the following workflow in principle: The physician examines medical images to make a diagnosis. Either, the CADx request is done automatically, e.g., by configuring an internal mechanism inside of the PACS, or the physician manually demands the CADx request. Data from the current patient’s context is then transferred to the CBIR system. The CBIR system processes the query input and generates a SR document from the CBIR results which is stored in PACS. The DICOM archive holds all SR documents and delivers requested CBIR results to the physician at his diagnostic workstation, who is awaiting the CBIR support for his diagnosis. The CBIR SR document lists identified images with a certain minimum similarity to the current examination image. Normally, the physician then requests diagnostic details of selected similar images from HIS manually to collect all relevant information for his decision making.

2.2 DICOM SR Encoded CBIR Results DICOM provides by means of the SR format a standard encoding of structured data. Templates define valid contents and value types to restrain different encoding of the same content in order to simplify the processing of SR documents. They facilitate an automated processing and interpretation of SR documents [20]. DICOM standard templates do not cover the CBIR application for CADx. We proposed a template adapted to the special requirements of CBIR [21]. It comprises the query image, identified similar images along with their similarity score, and a description of the applied CBIR system. Our template is applicable by any CBIR system and the resulting SR document may be stored to PACS.

2.3 Query of HL7 Diagnostic Findings HIS generally archives diagnostic findings from radiology, laboratories and other affiliated departments in a clinical repository. Reports may be plain text or encoded as, e.g., Portable Document Format (PDF), Microsoft Word. Communication regarding documents exchange is accomplished by HL7 messages. Message type QRYˆR02, “Query For Results Of Observation”, requests diagnostic findings, which are returned by message type ORFˆR04. A HL7 query message is composed by a message header (“MSH”), followed by a query definition (“QRD”) and a query filter (“QRF”). In clinical environments, HIS are usually configured to manage communication by a dedicated communication server. This implies that all HL7 messages are sent

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to this central point, specified by an IP address and a port. The header of the HL7 message contains the final destination, given in the field named “Receiving Application”. The communication server forwards the message to its addressee. The following small fragment of an examplary ORFˆR04 message is taken from a response to a QRYˆR02 message and contains requested diagnostic findings. Parts denoted by “...” have been ommitted to simplify the example. HL7 messages are divided into mandatory and optional segments and fields, depending on the particular message type. Each message begins with a header segment, introduced by the keyword “MSH”. The header of this example names “EKG” as “Sending Application” and our viewer “IRMACON” as “Receiving Application” of the message. Date of this message is 2010-02-18 and message type is “ORFˆR04”. The segment starting with “OBX” contains the actual diagnostic information and is of value type “TX”, which stands for text, followed by the “Observation Identifier” and the textual diagnostic information. MSH|^~\&|EKG||IRMACON||201002180944||ORF^R04|... ... OBX|1|TX|79000&ADT^EKG COMM|||... The actual diagnostic information has to be extracted from the message and to be displayed to the radiologist.

2.4 Mapping of DICOM and HL7 Identifiers The IRMACON viewer queries diagnostic findings by HL7 protocol that relate to patients and examinations whose medical images have been retrieved by the CBIR system. This requires a mapping of identifiers between the DICOM and the HL7 domain. Relevant keys are patient and order which are used in the HL7 query message to query particular diagnostic findings. There is no official standard that defines a mapping. But based on generally applied principles, e.g., by [16, 22], we decided to use the following mapping: • PACS Order Number – DICOM: (0008,0050) Accession Number – HL7: OBR-3 Filler Order Number • Patient Identifier – DICOM: (0010,0020) Patient ID – HL7: PID-3 Patient ID

2.5 Analysis of Data Capture Process We investigated the appropriate design of a viewer of similar medical cases and their corresponding diagnostic findings used in CADx. The following requirements have to be fulfilled in order for the radiologist to benefit from the viewer [23]:

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Fig. 1 Overview of the IRMACON system

• (R1) Presentation and arrangement of information must promote an easy and quick comprehension. This includes an appropriate structuring according to semantics and interrelations of data. Furthermore, the limitation on only relevant data and the provision of details only on demand helps to accelerate data capturing. • (R2) Handling of the viewer must be intuitive and simple. This allows a quick inital training and instant functionality recognition by the radiologist. • (R3) Presentation of data must be adapted to the particular application. For example, the identified similar images retrieved by the CBIR system are captured easily when presented pictorially. The corresponding DICOM identifiers are of little use in the context of CADx. • (R4) Data retrieval must not slow down the radiologist’s work. Otherwise, the physician will hardly be willing to use a CADx system.

3 Results 3.1 System Design Our proposed architecture is illustrated in Figure 1: 1. The radiologist at his diagnostic workstation starts the webpage of the IRMACON viewer, which is integrated into the PACS client as a plug-in by utilizing PACS’ application programming interface (API). The current patient’s context is passed to IRMACON. 2. The IRMACON viewer retrieves the SR document and all referenced images from PACS by DICOM C-MOVE messages. The images along with basic information are presented to the physician. 3. The physician may choose reports of diagnostic findings that are requested from the HIS by the IRMACON viewer. 4. The IRMACON viewer starts an appropriate application associated with the retrieved report to facilitate the display of the report’s content. Our system design is based on using the already established infrastructure by PACS and HIS. Data is transferred by DICOM and HL7 protocol. DICOM SR documents containing CBIR results are managed by PACS. Assuming that PACS and HIS are

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balanced systems configured for high performance and reliability, our design meets the requirement (R4).

3.2 Implementation of IRMACON Viewer The IRMACON viewer is a web-based application implemented in Hypertext Preprocessor (PHP) that dynamically generates output in Hypertext Markup Language (HTML) format. OFFIS DCMTK [24] is used for realizing DICOM commands from within IRMACON. HL7 messages are implemented using HAPI (HL7 Application Programming Interface) [25]. SR documents are converted to Extensible Markup Language (XML) by DCMTK and then parsed by the XML extension of PHP. The retrieved DICOM images are converted to Portable Network Graphics (PNG) in order to have an image format suitable for the representation in web browser. We created a testbed for our viewer limiting PACS and HIS to their relevant functionalities needed in our scenario. It includes a DICOM database accomplished by DCMTK configured with an DICOM Application Entity Title (AET) for accessing DICOM images and SR documents. Further, the HIS is simulated by a simple HL7 application. Our CBIR system of choice is the Image Retrieval in Medical Applications (IRMA) framework [26]. It has a Simple Object Access Protocol (SOAP) interface for transferring input data and results. CBIR output is created according to our SR template.

3.3 Layout of IRMACON Viewer The layout is illustrated in Figure 2: Fig. 2 Exemplary output of CBIR results in the IRMACON browser

1. At the top border, the query or examination image for diagnosis is shown. The identified similar images by the CBIR system are listed below in descending order of their similarity for easy comparison. This structures the information according to their semantics and interrelation, as postulated in (R1). Presenting on the main page images instead of textual data simplifies the capturing of the information (R3).

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2. Selecting an image opens a new window giving details on this image, namely examined body part, date of birth and sex. Furthermore, a button for retrieval of reports from the HIS is supplied. Providing further details only on demand meets (R1). 3. The navigation through the viewer is enabled by arrows pointing to the left for switching to images more similar or to the right to images less similar. Details are shown on pressing the field named “Select” on the bottom of the thumbnail. This enables an intuitive and easy handling as postulated by (R2).

4 Conclusions The introduced IRMACON viewer provides a comprehensive and consistent representation of CBIR results integrated into the clinical setting of a radiologist’s every day work. It assembles evidences sourced from CBIR, PACS and HIS necessary for diagnostic analyses. Hence, it follows the principal goal in health systems, “the right information, in the right place, at the right time” [27]. IRMACON establishes an essential link between CBIR systems and applied CADx. We hope that our proposal will contribute to the widespread use of CBIR for CADx in daily radiological routine. Our ongoing work comprises (i) the extension of our testbed and (ii) the processing of specified regions of interest for restricting the CBIR to a certain phenomenon. Acknowledgements. This research was partly funded by the German Research Foundation (DFG), Le 1108/9.

References 1. Smeulders, A.W.M., Worring, M., Santini, S., et al.: Content-based image retrieval at the end of the early years. IEEE Trans. Pattern Anal. Mach. Intell. 22(12), 1349–1380 (2000) 2. Doi, K.: Overview on research and development of computer-aided diagnostic schemes. Semin Ultrasound CT MR 25, 404–410 (2004) 3. Müller, H., Rosset, A., Garcia, A., et al.: Informatics in radiology (Inforad): Benefits of content-based visual data access in radiology. Radiographics 25(3), 849–858 (2005) 4. Müller, H., Michoux, N., et al.: A review of content-based image retrieval systems in medical applications – Clinical benefits and future directions. Int. J. Med. Inform. 73, 1–23 (2004) 5. Deselaers, T., Deserno, T.M., Müller, H.: Automatic medical image annotation in Image CLEF 2007: Overview, results, discussion. Pattern Recognit. Lett. 29(15), 1988–1995 (2008) 6. Nakayama, R., Abe, H., et al.: Potential usefulness of similar images in the differential diagnosis of clustered microcalcifications on mammograms. Radiology 253, 625–631 (2009) 7. Li, Q., Li, F., Shiraishi, J., et al.: Investigation of new psychophysical measures for evaluation of similar images on thoracic computed tomography for distinction between benign and malignant nodules. Med. Phys. 30(10), 2584–2593 (2003) 8. Muramatsu, C., Li, Q., et al.: Investigation of psychophysical measure for evaluation of similar images for mammographic masses: Preliminary results. Med. Phys. 32(7), 2295– 2304 (2005)

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9. Aisen, A.M., Broderick, L.S., Winer-Muram, H., et al.: Automated Storage and Retrieval of Thin-Section CT Images to Assist Diagnosis: System Description and Preliminary Assessment. Radiology 228, 265–270 (2003) 10. Zheng, B.: Computer-Aided Diagnosis in Mammography Using Content-Based Image Retrieval Approaches: Current Status and Future Perspectives. Algorithms 2, 828–849 (2009) 11. National Electrical Manufacturers Association, DICOM Part 16: Content Mapping Resource, http://medical.nema.org/medical/dicom/2009/09_16pu.pdf (Cited February 23, 2010) 12. Clunie, D.A.: DICOM Structured Reporting. PixelMed., Bangor PA (2000) 13. Philips Medical Systems, Integration of digital mammography on PACS (2007), http://www.healthcare.philips.com/phpwc/main/shared/assets/ documents/about/events/2009/ecr/pdf/hi/ integration_of_digital_mammography_on_pacs.pdf (Citied February 23, 2010) 14. Eastman Kodak Company, Make mammography work flow (2006), http:// www.carestreamhealth.com/mammoPACS_brochure_N1-102.pdf (Cited February 23, 2010) 15. Noumeir, R.: Benefits of the DICOM Structured Report. J. Digit. Imaging 19, 295–306 (2006) 16. Integrating the Healthcare Enterprise, IHE Technical Framework, vol. I: Integration Profiles (2008), http://www.ihe.net/Technical_Framework/upload/ ihe_tf_rev9-0ft_vol1_2008-06-27.pdf (Cited February 23, 2010) 17. Le, A., Mai, L., et al.: The workflow and procedures for automatic integration of a computer-aided diagnosis workstation with a clinical PACS with real world examples. In: Procs. SPIE, vol. 6919 (2008) 18. Welter, P., Deserno, T.M., et al.: Integration of CBIR in radiological routine in accordance with IHE. In: Procs. SPIE, vol. 7264 (2009) 19. Health Level Seven, Inc., HL7, Health Level 7 Standards (2010), http://www.hl7.org/implement/standards/index.cfm (Cited February 23, 2010) 20. Hussein, R., Engelmann, U., Schroeter, A., et al.: DICOM Structured Reporting: Part 1. Overview and characteristics. RadioGraphics 24(3), 891–896 (2004) 21. Welter, P., Deserno, T.M., et al.: Exemplary Design of a DICOM Structured Report Template for CBIR Integration into Radiological Routine. In: Procs. SPIE Medical Imaging, vol. 7628 (2010) 22. Kinsey, T.V., Horton, M.C., Lewis, T.E.: Interfacing the PACS and the HIS: Results of a 5-year Implementation. RadioGraphics 20, 883–891 (2000) 23. Dayhoff, R., Kirin, G., Pollock, S., et al.: Medical data capture and display: the importance of clinicians’ workstation design. In: Procs. Annu. Symp. Comput. Appl. Med. Care, pp. 541–545 (1994) 24. OFFIS, DICOM Toolkit DCMTK (2010), http://dicom.offis.de (Cited February 23, 2010) 25. University Health Network, HAPI (HL7 application programming interface) (2010), http://hl7api.sourceforge.net (Cited February 23, 2010) 26. Lehmann, T.M., Güld, M.O., Thies, C., et al.: Content based image retrieval in medical applications. Methods Inf. Med. 43(4), 354–361 (2004) 27. Winter, A., Lagemann, A., Budig, B., et al.: Integration of health professional workstation in hospital information systems. In: Procs. MIE, pp. 685–689 (1996)

3D Diagnostic System for Anatomical Structures Detection Based on a Parameterized Method of Body Surface Analysis Wojciech Glinkowski, Jakub Michonski, Robert Sitnik, and Marcin Witkowski

Abstract. Features of trunk and postural deformations are clinically observed to detect related musculoskeletal disorders, namely scoliosis, kyphosis or other thoracic deformities. High variability and controversial reliability of results of postural screening require new solutions to be employed. Standardized criteria for correct body posture are needed for further studies. The aim of this work was to present the current status of development of the 3D diagnostic system for anatomical structures detection. The designed system is based on a parameterized method of body surface analysis for automated measurement of the three-dimensional shape of patient’s trunk. This system uses structured light to measure patient’s body in 3D space by projection of a set of raster images on its surface. A unique feature of the presented system is the ability to operate on remote sites and carry out measurement interpretation by telemedicine utilizing a data warehouse. The system comprises of three independent modules which deal with measurement, data archiving and its analysis. Communication between modules is performed over the TCP/IP protocol, incorporating two different channels for each client, dedicated to two kinds of data - text channel, for transmission of XML documents used for delivering commands and information and binary channel for the transfer of large binary data, such as clouds of points or photographs. Presented modules altogether allow to measure the full shape of subject’s 3D surface along with measurement data storage and analysis for support of screening and diagnosis. Wojciech Glinkowski Medical University of Warsaw, Department of Orthopaedics and Traumology of Locomotor System, Center of Excellence "TeleOrto", Warsaw, Poland Medical University of Warsaw, Department of Descriptive and Clinical Anatomy, Warsaw, Poland Polish Telemedicine Society, Warsaw, Poland e-mail: [email protected] Jakub Michonski · Robert Sitnik · Marcin Witkowski Warsaw University of Technology, Institute of Micromechanics and Photonics, OGX, Warsaw, Poland E. Pi˛etka and J. Kawa (Eds.): Information Technologies in Biomedicine, AISC 69, pp. 153–164. c Springer-Verlag Berlin Heidelberg 2010 springerlink.com 

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1 Introduction Features of trunk and postural deformations are clinically observed to detect related musculoskeletal disorders, namely scoliosis, kyphosis or other thoracic deformities. Adolescent idiopathic scoliosis (AIS) is characterized by a complex lateral shift of the spinal curve in the frontal plane, associated with a complex 3D deformity of the trunk [28, 14]. Czech study by Kratenova et al. [15] performed on the group of children aged 7, 11, and 15 years has shown poor posture was diagnosed in 38.3% of children, more frequently in boys. Scapular protrusion (50%), hyperlordosis of lumbar spine (32%) and round back (31%) were found most frequently among cohort of children . A study performed on a group of students [4] has shown common presence of lumbar hypolordosis (71.0%, 48.1%F and 97.8%M), thoracic hyperkyphosis (round back) (58.0%, 53.7%F and 63.0%M) and very high prevalence of scoliosis (54.0%, 50%F and 58.7%M). These results require focusing on that problem having in mind high probability of postural deterioration in elderly. Among older adults and elderly aged 55-80 years, who had a Debrunner kyphometer measurement of kyphosis and supine lateral spine radiographs, the manual and digitized Cobb angle was 45 degrees (range 18 degrees-83 degrees), and the mean Debrunner kyphometer reading was 48 degrees (range 17 degrees-83 degrees) [12]. Saggital angles should be seriously considered because in older women with previous vertebral fractures hyperkyphosis is associated with an increased risk of mortality. The measurements of children and teenagers [30] have shown only 0.60% children aged 12 to 15 with correct body posture that requires consideration of standardized criteria required for further studies interpretation. Recent methods turning toward Evidence Based Medicine require meeting validity, reliability and quantitativity criteria. Previously described methods simplified measurements. Simple measurement of a number of 1.7 cm blocks required to place under patient’s head while lying flat to reduce hyper extension of cervical spine was practical allowing to define hyperkyphosis as requiring the use of one or more blocks [12, 13]. Other methods like inclinometry by simple reading may create no particular image to store for further monitoring. Considering both accurate measurement and data storage a combined method was developed to meet all the requirements. The aim of this work was to develop a 3D diagnostic system for anatomical structures detection based on a parameterized method of body surface analysis for automated measurement of the three-dimensional shape of the trunk in patients with deformations related to scoliosis, kyphosis and others. There are existing 3D measurement techniques with accompanying diagnostic algorithms. Moire photo-topography [24] was found in early 1980’s as the method suitable for 3D chest assessment. Fortin et al. used a structured light projection system to reconstruct a 3D surface of patient’s trunk to design a customized spinal brace [5]. Single-directional assessment of back curvatures screening has been elaborated in previous studies [25]. Poncet at al. reported that thoracic outline crosssections can be measured based on 3D data representing patient’s body surface captured with an optical measurement system [23]. However, the analysis method presented by them requires operator’s interaction and may imply human factor

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errors that depend on experience in 3D measurement data analysis or in clinical knowledge about pectus excavatum assessment. The clinicians are usually less familiar with new topographic surface shape measurements [15, 22]. In the last decades the equipment and software for surface measurements has evolved and turned into reliable 3 dimensions and high precision. The technology is approaching to meet clinical teams for further combined elaboration of a good consensus for surface measurements, a supplement for clinical studies. New multimodal evaluation with surface and radiological imaging shall bring new diagnostic dimension for future studies. Currently, direct comparison of radiological two-dimensional angular measurements (i.e. Cobb angle) and three-dimensional surface measurements may not show high correlation. Unequal back deformations may follow the Cobb angle [8, 10, 28] because surface measurements and x-rays do not measure the same aspect of the deformity. Gold standard parameters for surface topography require elaboration based on cooperation between engineers and clinicians to unify the parameters. Based on this principle the developed system uses structured light to measure 3D surface shape of patient’s body by projection of a set of raster images on its surface. Back shape only can also be subtracted from the exam to achieve comparable data to previous systems. Accurate 3D surface topography can help the clinician to measure spinal deformity at baseline and monitor changes over time. It can help to turn the patients and their families’ awareness to the deformity problem.

2 Telescreening Diagnostic System Remote screening was described for a few disorders in otology, ophthalmology, and endoscopy but rarely for musculoskeletal problems [3, 5, 7, 11, 14, 19, 27]. The firstly reported screening for scoliosis begun in 1963 in Aitken, Minnesota, USA [18]. Screening of postural deformations is discussed in the literature frequently. Review of screening methods and policies was published recently [9]. School screening to identify children at risk for scoliosis is mandated in many countries. However, there exists some controversy on the effectiveness of routine scoliosis screening [9]. Orthopaedic societies (AAOS, SRS, POSNA, and AAP) in 2007 recognized that support for scoliosis screening has limitations, but the potential benefits that patients with idiopathic scoliosis receive from early treatment of their deformities can be substantial. Scoliosis screening, whether in the physician’s office, nurses’ clinics, or school environment, provides the opportunity to diagnose the condition and make referral for appropriate medical care. Females should be screened for scoliosis twice, at the age of 10 and 12, and boys once, at the age of 13 or 14. School screening personnel should be educated in the detection of spinal deformity. No single test is completely reliable for screening scoliosis but the forward bending test should be always included. Considerable screening judgment should avoid unnecessary referrals. Deformities screening among elderly may achieve a stronger feedback due to rise of mortality rate among hyperkyphotic fallers with osteoporotic fractures. In United States the total costs of medical care of scoliosis rise from one monetary unit per child screened, to 122,05 per identified case, 439,39

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per child treated. Optical methods used for clinical screening attract investigators in concern of radiation exposure that the children may have undergone following clinical screening. Approaching toward the general trend of reliable screening the 3D diagnostic system is developed. Proposed solution consists of three main modules: four one-directional measurement systems, a database and a set of numerical tools for medical diagnosis support. The measurement system is designed to measure full patient body shape in a specialized laboratory by four measurement heads but also it can work in screening mode where two measurement heads can be easily transported and calibrated in any location. Authors plan to measure 20 000 children in Polish schools in screening mode and selected cases will be re-measured using the laboratory system. The system consists of three independent modules (Fig. 1). Each of the modules has a certain type of input and output and together they form a complete data processing path. The measurement module returns a generalized measurement in the form of cloud of points, the archiving module can be customized arbitrarily to store information characteristic for specific application and the analysis module can be programmed to get all the necessary features from the data. The modules communicate with each other using a TCP/IP network.

Fig. 1 Modular structure of the system

The system allows working in on-line and off-line mode. Off-line mode is used when there is no Internet connection available in remote location. In this case the measurement data and patient information are stored locally and synchronized automatically just after establishing connection with the database. Parameters supporting medical diagnosis are calculated from measurement data representing surface shape of patient’s body. First the curvature maps are calculated and on the base of their values distribution required anatomical structures are localized. Finally, from the positions of the anatomical structures final parameters are extracted [1, 2, 20, 21].

2.1 Measurement System The measurement system consists of four modules which simultaneously measure patient’s skin surface from four directions. Each directional module is an optical full-field 3D scanner based on structured light projection method. The main components of each module are: projection unit, which is a Digital Light Processing (DLP) projector, detection unit which is a Charge Coupled Device (CCD) or a

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Complementary Metal-Oxide-Semiconductor (CMOS) camera and a PC-class computer (Fig. 2(a), 2(b)). During the measurement process the patient is placed inside a calibrated measurement volume while a series of patterns is projected onto his or her body surface. These patterns include sinusoidal fringes and modified binary Gray codes. The shape of body surface is calculated based on the raster deformation according to the Temporal Phase Shifting (TPS) method [27]. Dataset produced by the measurement system is in the form of a set of (x, y, z) points that represent the sampled surface of patient’s body.

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Fig. 2 A visualization of the measurement system (a) and the measurement volume (b)

The electro-optical hardware setup utilizes TDP-MT700 projectors by Toshiba Corp. and Flea B&W cameras by Point Grey Research Inc. (Fig. 3(a)). In order to avoid interferences caused by the overlapping of raster images originating from adjacent projectors spectral filters are mounted on projector and detector lenses. This allows to project raster images simultaneously (Fig. 3(b), 3(c)) and conduct measurements using all modules at the same time. The metrological values of the measurement system are as follows: • measurement volume size: scalable from 1.0m x 1.0m x 1.0m to 1.5m x 1.5m x 2.0m, • accuracy: 0.2mm to 0.4mm (depending on the measurement volume size), • data acquisition time: 0.7s (all modules simultaneously), • maximum number of points: 4 million. Depending on the size and position of the calibrated measurement volume the resulting point cloud may represent patient’s thoraco-abdominal region or the whole body surface (Fig. 4). Measurement data acquired with use of the measurement system along with patient’s textual data are stored in a dedicated database.

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(a)

(b)

(c)

Fig. 3 The measurement setup built: (a) a directional measurement module fixed to a stand, (b) a healthy individual illuminated with fringe patterns, (c) magnified fringes projected by two adjacent measurement modules

Fig. 4 A three-dimensional point cloud representing body surface measured with the four-directional measurement system

2.2 Database The database is the heart of the system and serves two main purposes - archiving of data and guarding it from unauthorized access. All operations on the database are performed using a specially designed XML interface, which makes the system independent of the underlying database implementation. The interface fulfills different functions, including user authentication, data import and user queries. Moreover, the structure within the database can be in full defined using XML without any necessary knowledge about the system itself and can be extended on the fly in case any additional information or data is required. Data can be assigned to three main groups - objects, which are the core entities keeping data universal during system’s lifetime, data elements, which are supposed to be assigned to each object, keeping information variable in time, and additional

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elements which are all kinds of data derived from the original data elements. The elements can further be linked with each other in an arbitrary way, thus creating a hierarchical structure. The structure (division into groups and linkage of elements) used in this case is shown in Fig. 5.

Fig. 5 Structure of elements within the database

The XML standard also provides a very robust yet easily-definable way for the construction of user queries for the data, including different types of value and linkage constraints and requests for any part of each element. Communication between modules is performed over the TCP/IP protocol, incorporating two different channels for each client, dedicated to two kinds of data - text channel, for transmission of the XML documents and binary channel for the transfer of large binary data, such as clouds of points or photographs (Fig. 6). Such a structure is asynchronous and allows performing traffic inexpensive operations such as user logon or querying for text data independently of binary transmission, very costly in terms of network transfer. To further decrease this cost data compression was implemented and was also incorporated in data storage.

Fig. 6 Communication between modules

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A user account system was also created, providing not only authentication, but also authorization of users, which allows to limit some of them to a read-only mode, even on a per element or per field basis. These features altogether form a complete system which can be securely used over any network, be it a local area network (LAN) or the Internet.

2.3 Calculation and Diagnosis Support The data gathering and analysis module provides a complete interface for the database, allowing the user to manage the information and perform certain operations on the archived measurements. It supports automatic analysis - so called pattern calculation - a series of operations that can be automatically performed on a subset of data according to a predefined scheme. The module is constructed in a way which assures that no data becomes overwritten - any number of derived information can be saved in the database and linked to the parent measurement, thus keeping it consistent and easy to browse. It also makes it possible to compare different measurements, allowing the estimation of patient’s improvement in time. This requires good repeatability of measurement and a method to correlate two measurements of the same patient in space. System’s vertical, additionally measured every time an examination is carried out and assigned to measurement, and two points within the measurement are sufficient for absolute alignment. Since fine alignment uses two landmarks (dimples of pelvis) for accurate positioning, it is preceded by a coarse operation which detects the general position of the body. Analysis can be carried out in two ways - discrete, based on a set of landmarks on the surface of the body or on a more global shape analysis. The discrete analysis itself can be performed either using manual indication of points or an algorithm of automatic landmark detection. Such algorithms are currently under development, at the moment the landmarks are acquired from a team of trained physicians, which will help in the development process and provide the assessment of algorithms’ reliability. Additionally, the points provide interesting information about the interobserver and intraobserver reliability for evaluated measurements. A preliminary algorithm for automatic landmark extraction is built upon a modified back diagram for a number of predefined landmarks, of which starting positions are precalculated using an averaged set of manually selected points, scaled for each measurement with respect to a simple bounding box generated around it (Fig. 7). Such a processing path is easily extendable to an arbitrary number of characteristic points, thus providing a versatile detection method. The method assigns an area to each landmark, within which the exact position of the landmark is searched for. The 3D shape contained in each cell is analyzed based on maps of parameters C1 and C2, which give general information about surface shape.

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Fig. 7 A visualization of a modified back diagram generated for 12 back landmarks

These parameters were developed in order to describe surface shape of full 3D point clouds [31]. The C1 parameter describes how much the surface in the neighborhood of the considered point deviates from a plane, its values are positive for convex areas, negative for concave areas and zero for planes (Fig. 8(a)). The C2 parameter describes the distribution of normal vectors in the neighborhood of the considered point in a way allowing distinguishing areas of unidirectional curvature, such as cylindrical areas, and omnidirectional curvature, such as spherical areas and takes values equal to zero for planes and cylindrical surfaces and positive for other surface types. The highest values of C2 are obtained for sphere and for saddle shapes (Fig. 8(b)).

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Fig. 8 A distribution map of (a) C1 (b) C2 parameter over body surface (real measurement data)

The analysis of distribution of C1 and C2 parameter values allows discrimination of various surface types in a way similar to used with mean and Gaussian curvatures, yet the former are faster to calculate and more resistant to noise in the analyzed dataset.

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Division of the back into subregions makes it possible to avoid global analysis of the back surface. Moreover, the landmarks are not exactly points, but are regarded as certain regions on the surface of various scales and as such require computation of the C1 and C2 maps with different input parameters. Each landmark also exhibits specific properties depending on the type of posture which implies the use of different detection paths and an algorithm which would provide some general, coarse information about the posture of the patient, or possibly an adaptive path of detection which would modify its parameters based on some overall properties of the shape of the back. An additional potentially interesting feature is the possibility of comparison of the 3D shape with volumetric data, such as a CT scan.

3 Conclusions In this paper a complex solution for diagnostic and screening of three-dimensional assessment of human body, mostly trunk and its postural deformities has been described. It allows to measure full shape of subject’s body 3D surface along with measurement data storage and analysis for support of screening and diagnosis. Described system is still in the development stage, especially in the areas of final automated data analysis and clinical validation. However, for selected cases some clinical validation has proved that author’s concept is correct. Future works will be focused on the following tasks: • Further optimization of anatomical landmarks localization and its verification for different subject types in whole population (males, females, children, elderly), • Comparison of existing anatomical parameters versus specialist votes, • Continuous extending of diagnosis scenarios along with its clinical validation. Acknowledgements. The project is supported by grant number NR13-0020-04/2008 from the Ministry of Science and Higher Education.

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Reconstruction of the Pelvic Region Based on the Statistical Shape Modeling Pawel Skadlubowicz, Zdzislaw Krol, Zygmunt Wrobel, Fritz Hefti, and Andreas Krieg

Abstract. Up until now the reconstruction of the pelvis defects after bone tumor resection has typically been by autologous or allogenous grafts. These approaches were highly unsatisfied because of large shape differences between the harvested transplant and the site to be reconstructed. There exists a huge demand for patient-specific and anatomically shaped implants. In this paper we propose a new pelvis reconstruction planning approach based on the statistical shape modeling. For generation of the statistical pelvis shape model a large data pool of CT datasets has been collected. Afterwards, the CT data segmentation and surface processing methods delivered the required pelvis geometries. Via Procrustes analysis of the collected pelvis surfaces the parameterized pelvis shape mean model has been calculated and the principal component analysis (PCA) [4] applied for estimating the anatomically optimal graft or implant geometry. In this work we demonstrate on a clinical pelvis reconstruction case that the using of statistical shape models in the oncologic surgery planning is a robust and very promising method. A quantitative evaluation of the matching quality and the convergence process is given.

1 Introduction The pelvis oncologic surgery is beside the radiotherapy the most common treatment of malignant bone tumors. Pelvis is one of the principal components of the human locomotor system therefore its reconstruction after resection of malignant Pawel Skadlubowicz · Zygmunt Wrobel Department of Biomedical Computer Systems, Faculty of Computer Science and Materials Science, University of Silesia, Sosnowiec, Poland e-mail: [email protected], [email protected] Zdzislaw Krol · Fritz Hefti · Andreas Krieg Pediatric Orthopedic Department, University Children’s Hospital Basel (UKBB), Basel, Switzerland e-mail: [email protected], [email protected], [email protected]

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pelvic tumors presents a highly complex and challenging problem. One of the main problems is the shape definition of artificial implants or autologous transplants for anatomically optimal reconstruction of the resected osseous part. The analysis of the anatomical shape and statistical shape modeling is a wide area of investigation. In the past many authors have developed statistical shape models for different anatomical structures (see for instance [5, 6, 11] and [13]). The objective of this paper is to investigate the use of statistical shape models in the preoperative surgery planning for pelvis reconstruction. In the following a new reconstruction methodology based on the deformable pelvis statistical shape model including a novel optimization approach based on the genetic algorithms [8] will be described and explained. A quantitative analysis of a clinical planning case will be given.

2 Methods Among many planning approaches for reconstruction of the resected part of the pelvis the mirroring method is the most widely used computer-aided surgery planning procedure in the reconstructive surgery. It is based on the preoperatively acquired computed tomography (CT) dataset of the patient. After segmentation of the unaffected side a mirrored surface is aligned with the defected region. It enables fast generation of an anatomically similar model of the target region. The disadvantage of this method is the natural asymmetry in human anatomy and the fact that the existing osseous structures on the unaffected side are often malformed due to increase of load on the healthy side. The additional limitation is that this method can be applied to unilateral defects only. The bilateral defects still remain a challenging problem in the reconstructive pelvic surgery planning.

Fig. 1 The data processing pipeline for generation of our statistical pelvis shape model

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The proposed new planning approach is based not only on the patient single CT dataset for the fitting the designed implant shape to the existing osseous structures but uses the statistical pelvis shape model for the optimal reconstruction of the morphological region of interest (ROI). For generating the statistical pelvis shape model one need a large data pool of pelvis CT datasets. The required pelvis geometries (called training set [2]) are obtained via segmentation and surface processing methods. Different stages of the data processing pipeline for generation of the statistical pelvis shape model are presented in Fig. 1. In the following section a brief overview of the statistical shape model generation process will be presented. We will explain the main stages of the method: segmentation, surface mesh processing, data alignment and the principal component analysis. Our training set for the pelvis statistical shape model has been generated using a CT data pool (n = 20) collected at our hospitals. In our approach the pelvis shapes are described by triangular mesh surfaces. The generation of the training set is done via segmentation of all the CT data. Various segmentation methods implemented in our self developed segmentation, visualization and modeling system SeVisMo [10] has been used for generation of the training set. Various region growing segmentation methods like for example: connected threshold, neighborhood connected, confidence connected and isolated connected one; flood fill methods, mask operations as well as the manual segmentation tools were required to identify and separate the all required osseous structures in the pelvis region (left pelvis, right pelvis, sacrum, right femur and left femur) from all acquired CT datasets (see Fig. 2). In Fig. 3 are presented five different left pelvis bones segmented using the mentioned above methods and belonging to our pelvis shape training set. Notice the noticeable shape variability in the ilium and acetabulum regions.

Fig. 2 Segmentation stage of the patient CT data with a tumorous lesion at the left ischiopubic ramus (red circle): (a) oseous structures (green) segmented using the connected threshold method, (b) manually separated bones, (c) masks with filled internal structure of bones, final stage of the segmentation process, (d) color coded surface mesh representation of the segmented bones, generated using the marching cubes algorithm [7]

Upon the segmentation stage and still before the incorporation into the training set the triangular mesh surfaces are undergone special processing and optimization. The surface mesh representation of the segmented bones is generated by the marching cubes algorithm [7]. Because the CT data sets are noisy and could contain different imaging artifacts the following surface mesh processing methods are

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Fig. 3 Five triangular mesh surfaces of the left part of pelvis bone segmented from our pelvis CT datasets and belonging to our training set. One can observe for instance different shapes and sizes of the acetabulum.

required for improving the surface mesh quality: cleaning, smoothing, remeshing and decimating. The next stage in our data processing pipeline is the establishing of correspondence betwen different pelvis shapes for statistical analysis. First and foremost, the same number of nodes in all anatomically corresponding meshes of the training set must be achieved. In our approach it will be assured by using the thin plate spline transformation [1]. We choose from the training set the surface mesh which is the best anatomical representation of the pelvis. This base surface mesh is then elastically matched with each of the pelvis surfaces from the training set. In this way we obtain approximated copies of the original pelvis surfaces but they all have now the same number of nodes. In Fig. 4 below are presented the effects of the thin plate spline transformation applied to one of the surfaces from our training set. After

Fig. 4 Two instances of the left pelvis bone from the training set before alignment. The grey bone surface is the target surface and the green one is the source surface (a), the corresponding landmarks for both surfaces (pre-match status) are colored red and green (b), the aligned surfaces after applying the thin plate spline transformation (the green surface has been deformed) (c).

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establishing the correspondence between different shapes from the training set, a Procrustes analysis and the PCA [3, 4] method are performed, resulting in a mean pelvis shape model and in the most dominant modes of variation. Our pelvis statistical shape model P is defined in the following way: n

P = P0 + ∑ λk Dk

(1)

k=1

where P0 is the mean pelvis shape model representation and λk is the eigenvector matrix characterizing the prior information. Changing the deformation parameters Dk , allows us to get a model instance, which is a deformed version of the mean model P0 . Our statistical hemi-pelvis shape model has been built from the twenty training pelvis mesh surfaces. In Fig. 5 the shape changes corresponding to the first three principal modes of variation are presented. In the following we will demonstrate on a clinical case how the generated pelvis statistical shape model allows estimating the optimal morphological target geometry for arbitrary region of interest to be reconstructed. The implementation of the described approach in the SeVisMo [10] is based in part on the Vtk library [12]. For the establishing of the correspondence between different instances of the pelvis in the training set two Vtk classes has been used: vtkIterativeClosestPointTransform and vtkThinPlateSplineTransform. Vtk also includes classes dedicated for generation of the statistical shape model. vtkProcrustesAlignmentFilter and vtkPCAAnalysisFilter are filters making possible the application of PCA to 3D surface meshes. These two methods have been implemented in our application too. The described above surface matching method (using the thin plate spline transformation) plays also a crucial role in the reconstruction of the resected pelvis defect. An automatic optimization method delivering the anatomically best shape for the pelvis reconstruction uses the genetic algorithms as the optimization engine [9]. This powerfull aproach has been choosen because of limitations of the classical optimization methods. The limitations are mostly connected with target function. Particularly an analytic form is required and in many cases first and even second derivative as well.

3 Results and Discussion The explained above surgery planning approach based on the statistical shape model has been applied to find the anatomically optimal bone shape for reconstruction of the pelvis after tumor resection (see Fig. 6). The estimation of the optimal matching transformation parameters has been done by applying the non-deterministic optimization method: genetic algorithms. The demonstrated application of the surgery planning method based on the statistical shape model shows that the reconstruction of the resected pelvis bone is successful and strongly correlates with the anatomical shape of the region of interest. The presented in Fig. 5 pelvis models also demonstrate the robustness of the

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Fig. 5 Demonstration of the shape changes corresponding to the first three principal modes of variation The left pelvis bone generated using our pelvis statistical shape model for different values of variation modes: 0.0, 0.0, 0.0 (a), -1.0, -1.0, 0.0 (b), -2.0, 0.0, 0.0 (c), 0.0, -1.0, 0.0 (d), 0.0, 0.0, 2.0 (e), 1.0, 1.0, 1.0 (f), 0.0, 1.0, -2.0 (g), 0.0, 0.0, -2.0 (h).

Fig. 6 Application of the planning approach for the clinical data (tumorous lesion at the left ischiopubic ramus). Virtual resection of the bone tumor (left and center). Statistical shape model matched with the patient pelvis model (right).

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Fig. 7 Color coded deviation [mm] of the matched surface from the target surface